What are the important things that we should be aware when we are awake and learning all night on Shavuot?
Based on the Arizal, learning should first include learning the Tanach, 613 Mitzvot, Midrash, and after that, האידרא רבא and passages from the Zohar HaKadosh because it is explicitly written in the Zohar "And the end is as arranged in the books of the Tikkun" (Ben Ish Chai Parashat Bamidbar). We already know the minhag of the chida zichron livracha to learn on this night the two idronot standing up even if you are old. The person who does this, their reward is great (Ben ish chai there).
You should not learn Mishnayot on Shavuot night and one who has a set custom to learn 18 chapters of Mishnayot every day may specifically do the eighteen chapters during the day but not during the night. There is nothing to prevent learning the Mishna, you should not do so the night of Shavuot. With any other night (I.e Shabbat or the rest of the Yom Tov) there is nothing preventing to learn Mishna at night.(Ben ish chai). Yeshiva students who want to learn Talmud or someone who is not able to stay up throughout the night, at least they should learn the Tanach arranged in the Tikkun, passages from the Midrash, passages from the Zohar and a little bit of the six hundred thirteen mitzvot .
If someone is learning Torah all night, and are served tea, coffee, etc, they should make blessing the first time they had a drink during the night. They should not make another blessing when they are served another cup even if it has been more than fifteen minutes between each cup. They are exempt from making another blessing after the first time. It is good to state explicitly beforehand, that their first bracha covers all of their other cups they may be drinking that night.
However, if someone leaves the synagogue to take a break, and then returns, they should make another bracha because leaving the synagogue is considered a distraction
Some people read the Shema on the night of Shavuot, before חצות. This is our custom at Etz Ahaim.
You should say the morning blessings after Alot HaShachar (4:15am), and if a person didn't sleep the whole night of Shavuot, they can still say the morning blessings of the Torah after Alot HaShachar. Aside from the blessings of the Torah, some people do all of the morning blessings including Elokai Neshama, but exclude Al Netilat Yadayim, because a person who did not sleep at night washes their hands without a bracha.
The פרי מגדים writes in סימן תצד that on the holiday of Shavuot, when we are awake all night, we are permitted to pray before נץ because if a person goes back home first, it will be a burden to wake them up to make a minyan. Nevertheless some people are careful not to read the Shema early in the morning. The Shulchan Aruch in סימן נח writes that you are able to Read Shema already from Alot HaShachar.