1. Birkat HaTorah

The Rishonim give two reasons for saying Birkat HaTorah every morning:

The Rosh (Rabbenu Asher) on Masechet Brachot (1, 13) wrote that sleeping – even in the afternoon – constitutes a hefsek (interruption) to Birkat HaTorah. That is, when one says Birkat HaTorah, as long as he didn't have hese'ach hada'at (an interruption of attention) from the Torah, the blessing is still in effect. The Gemara in Masechet Brachot (35b) says that this is true even according to Rabbi Ishmael who holds that it is permitted to combine Torah with work, and said "act with derech eretz regarding them." And Rabbi Chaim of Volozin explained that the expression "act with derech eretz regarding them" means that even though a man is permitted to work for his living, while he is working his thoughts should mainly be on Divrei Torah. Therefore according to the Rosh, even when one eats and works, his attention is not interrupted from Divrei Torah, but when he goes to sleep one doesn't have da'at (cognition) and therefore according to his opinion, we should be required to say Birkat HaTorah even after sleep in the afternoon.

Tosefot on Brachot (11b) bring the opinion of the opinion of Rabbenu Tam, who explained that we say Birkat HaTorah every morning because the takanah (Rabbinic amendment) is to say Birkat HaTorah every 24 hours.

True, generally the day goes after the night (for example, Shabbat begins at sundown), but in this case the night goes after the day. A source for this can be brought from the Gemara in Eruvin (65a) which says that Rav Acha Bar Yaakov would borrow during the day and pay at night. That is to say, he would work during the day, and since we should learn Torah all day, he would make up the Torah learning at night. We see that Torah learning at night is the time of "paying the debt" from the day, and therefore the night goes after the day.

Regarding one who sleeps in his bed during the day, the Shulchan Aruch (Orach Chayim 47,11) mentions the opinion of the Rosh, but writes according to Rabbenu Tam's opinion that sleep isn't considered an interruption.

 (We can explain that only a night's sleep is considered an interruption, but sleep during the day is shorter and its purpose is to regain strength in order to continue learning Torah. A story is told about Reb Shlomo Zalman Auerbach ztz"l: One time he was tired before a shiur he was to give, and he told his wife that he had to sleep, and if anyone would ask where he was, she was to say that he was preparing the shiur. Reb Shlomo Zalman explained to his wife that this wasn't considered lying because sleeping really helps him get ready for the shiur!

In any case, according to all opinions, sleep at night in one's bed is considered an interruption, and this is the reason that we say Birkat HaTorah every morning.

The practical difference between the Rosh and Rabbenu Tam arises when one doesn't sleep at all at night. According to the Rosh there was no interruption, and he cannot say the blessing. According to Rabbenu Tam, since a new day began, he can say the blessing.

The poskim offer several solutions to the problem of being awake all night on Shavuot:

The Mishna Berura (47,28) wrote that one can find a person who slept half an hour in his bed and be yotzei by hearing his blessing. In this case the one who was awake should make a condition that if he isn't required to say the blessing, then he only intends to answer "Amen" on hearing someone else's blessing.

A suggestion brought by the Gaon Rabbi Akiva Eiger (in his annotations to the Shulchan Aruch) and his son-in-law the Chatam Sofer is to sleep on the afternoon of Erev Shavuot and then be obligated to say the blessing the next morning since mi mah nafshach (in this situation there is no difference between the opinions of the Rishonim) – and also according to the Rosh, the afternoon sleep was an interruption.

There are questions which can be raised regarding this suggestion, based on the words of the students of Rabbenu Yonah in Brachot, who said that "Ahavat Olam" of the evening prayer is itself considered as Birkat HaTorah, and therefore according to the Rosh, when he said it (the previous night) he was yotzei. And we can explain according to the Yerushalmi which the Tosafot quoted in Brachot (11b) that Ahavat Olam exempts one from Birkat HaTorah only if he learns Torah immediately afterwards, and the Shulchan Aruch questions whether Kriat Sh'ma is considered learning Torah, and therefore perhaps if he doesn't learn after Ahavat Olam, then Rabbi Akiva Eiger's solution is effective.

 (Alternatively): Not to say Birkat HaTorah in the morning, and to intend to be yotzei with the blessing Ahavah Rabbah and immediately afterwards to learn something.

Luach Eretz Israel quotes the Aderet, the father-in-law of HaRav Kook ztz"l as saying that even according to the Rosh, one can have intention that Birkat HaTorah which he says will remain in effect until the next morning, in spite of the interruption. And this explanation is a chidush and there is considerable difficulty regarding it.

In practice:

For Ashkenazim – it is best to hear the blessing from another person who has slept, and if this isn't possible, one can rely on the solution of HaGaon Rabbi Akiva Eiger. There are also Ashkenazi poskim who rule that if one doesn't have another person, he can say Birkat HaTorah himself (HaGaon Rabbi Shlomo Zalman Ohrbach, Aruch HaShulchan and others), and this is based on Sefardic poskim.

The Sefardic poskim (Kaf HaChaim, Yabiya Omer) hold that the essential halacha is according to Rabbenu Tam, as such was the accepted custom over the generations. And Terumat HaDeshen (ch. 37) writes that where there is a minhag, we don't say safek brachot lehakel (where there is a doubt about a blessing, one should not say it) and therefore the Sefardic custom is that one who didn't sleep all night says all the brachot as usual – with the exception of netillat yadayim which isn't said, and asher yatzar is he didn't need to relieve himself.

Ashkenazim do not say Birkat HaTorah, and there is a debate regarding the blessings "Elokai neshama" and HaMa'avir sheinah" – according to the Sha'arei Teshuvah one doesn't say them, and according to Shulchan Aruch HaRav these blessings are said.

1. The Custom of Eating Dairy Foods

The Mishnah Berurah (ch. 494) brings an interesting reason for eating dairy foods on Shavuot: when Am Israel received the Torah, they couldn't eat anything except dairy products, because meat requires time-consuming preparations: a proper and checked knife for slaughtering, nikur (extracting forbidden parts from the meat), hadachah (removing blood) and more. Therefore at that time it was preferable to each dairy products, and in memory of this we eat dairy foods on Shavuot.

A different reason is brought in the book T'vuot Shor. The Gemara in Shabbat (88a) tells that when Moshe went up to heaven, the angels didn't want G-d to give Torah to flesh and blood.  The Midrash says that G-d answered them that when they will descend they will eat meat and milk by Avraham, and even Jewish schoolchildren are careful about separating between them. Therefore we eat dairy on Shavuot to remember this.

In practice:

Since it is a mitzvah to eat meat on Yom tov, the custom is to eat dairy foods in the morning and at noon a meat meal.

Regarding the separation of meat from milk:

The Gemara in Chulin (105a) says that if one ate meat, it is forbidden to eat cheese, but if one ate cheese it is permitted to eat meat. And Rashi explains that meat secretes grease and therefore one must wait, but cheese does not remain in the mouth very long, and therefore it is permitted to eat meat afterwards.

The Rambam writes that meat gets stuck in the teeth and therefore it is forbidden to eat dairy afterwards, but after 6 hours the remnants of the meat are no longer considered meat.

There is a disagreement between the Rishonim regarding how long one must wait between meat and milk.

Tosefot in Chulin (104b) in the name of Rabbenu Tam, Ba'al Halachot Gedolot, Rabbi Zerachiah HaLevi and the Re'em hold that after one cleaned his mouth and rinsed his hands he can eat cheese immediately. Conversely, after eating cheese one can eat meat immediately even without cleaning and rinsing.

The Rif, the Rambam and the Rashba ruled that after eating meat, one must wait 6 hours before eating cheese, and in order to eat meat after cheese it is necessary to clean and rinse the mouth, and then one can eat meat immediately.

The Shulchan Aruch in Yoreh De'ah (89,2) rules like them. The Ramah adds that there are those who are stringent after eating hard cheese to wait as between meat and milk, and some Ashkenazim keep this custom. But the regular yellow cheeses which are sold in our supermarkets are not the hard cheeses which the Ramah refers to.

Today there is a widespread custom to wait between dairy and milk half an hour or an hour. Where did this minhag come from?

The Beit Yosef in Orach Chayim (ch. 173) quotes the Zohar from Parshat Mishpatim which says not to eat meat and milk together and not in the same meal, as this arouses dinim (decrees) in the world.

There are those who understood that one must wait between milk and meat, and others who understood this as meaning that they shouldn't be eaten at the same time and we must make a hefsek (interruption). What is considered a hefsek? Rashi (Pesachim 99b) writes that "immediately" is considered within half an hour, and more than that is considered a hefsek. And it is universal that in every other situation we consider half an hour a hefsek. These are the sources for the customs to wait half an hour and an hour.

In practice:

Regarding the basic law, the Shulchan Aruch rules that if one said Bracha Acharonah, rinsed his hands and cleaned his mouth, he can eat meat immediately after cheese. But if we take into account the opinion of the Zohar HaKadosh, this isn't sufficient because of the mystical factor, which causes spiritual damage. Therefore from the halachic side, we only have the ruling of the Shulchan Aruch, but it is proper to act according to the Zohar as a midat chassidut, and the Shla"h wrote accordingly, that one who waits half an hour or an hour, a blessing will come upon him.

    3. Using a Stove Top on Yom Tov

There is a type of gas burner with an electric ignition, and in order to turn the gas knob it is necessary to push the button which ignites the flame, and if the ignition button isn't pushed, the gas knob will not turn (in order to prevent gas leaks). How can this kind of burner be used on Yom Tov? The book Ohr LeTzion offers a suggestion:

The Shulchan Aruch (Orach Chaim 502, 1) rules that it is forbidden to light fire on Yom Tov, and there is a debate as to whether this prohibition is from the Torah or a Rabbinic decree.

The Ta"z (at the beginning of ch. 502) holds that the prohibition is from the Torah, and the definition of Ochel Nefesh (preparation of food which is permitted on Yom Tov for consumption on Yom Tov) is preparation, like cooking and baking, which is "yesh mi-yesh" (using existing materials). But lighting fire is "yesh mi-ayin" (creating a new thing which didn't previously exist) and this is not permitted on Yom Tov. But the majority of Acharonim disagree and hold that lighting fire is permitted from the Torah, but because it resembles the prohibition of "molid" (creating something new) the Rabbis decreed not to light fire on Yom Tov. Additionally, fire can easily be prepared before Yom Tov.

There is a great practical significance as to whether, in a situation of need, we can tell a non-Jew to light fire. On Shabbat this is definitely forbidden because amirah l'nochri (telling a goy to do melachah) is prohibited because of shevut (a range of Rabbinic prohibitions, related because of their similarity and/or connection with Torah-prohibited melachah). But on Yom Tov: according to the Taz it is prohibited like on Shabbat, but according to most Acharonim, who hold that the prohibition to light fire is a Rabbinic proscription, the Shulchan Aruch has already ruled that amirah l'nochri regarding shevut is permitted in the case of illness or loss. Additionally, according to Ba'al Ha'Itur as brought in the Shulchan Aruch (276, 2) a goy can be told, even regarding a Torah prohibition for the purpose of a Mitzvah. The Ramah quotes this and writes that we don't rely on this except for a great need. And we can attribute to this a "safek s'fekah" (double uncertainty): 1) perhaps the halacha is that the prohibition is Rabbinical, as most Acharonim rule, and 2) if the halacha is according to the Taz (that the prohibition is from the Torah), perhaps the halacha is (also) according to Baal Ha'Itur.

Additionally, in Morocco (as brought in the book Shemesh uMagen) the custom was to switch on electricity on Yom Tov because they claimed that electricity already exists in the wires and it only needs to be exposed, and one who switches it on merely transfers fire and doesn't create it. (Their intention was not that the electricity already existed, but that the Torah only prohibits fire created by striking stones, which is a severe action.) Ultimately, the halacha is not according to their line of thought, and many Acharonim dispute with them regarding the definition, but we can add their opinion to the leniency of telling a goy when there is a need.

Therefore, the Ohr LeTzion says: since the primary opinion is that the prohibition of lighting fire is Rabbinic, if a Jew will put a burning match to a gas burner of the type we mentioned above before ignition, and will turn the knob (while at the same time pressing the ignition button), since he already has fire burning from the match and he only needs the gas and not the fire from the ignitor – then the pressing of the button is p'sik reisha d'lo ichpat leih (an inevitable outcome which he doesn't care about) in a rabbinic prohibition, and Tosefot (Shabbat 113a) rule that this is permitted, especially if we add the opinion of the Rabbis of Morocco to the leniency. We must note that this leniency is permitted only to the Sefardic community, since the Askenazim are stringent to require "trei d'Rabanan" (a case where the prohibition is the result of two Rabbinic restrictions).