1) A belt is sufficient, unless you (or your father) has the minhag to wear a gartel (e.g., Chassidim).
2) Ideally, start at the exact same time. If not, it is still tefilla b’tzibbur [according to Rav Shlomo Zalman Auerbach] if they are (in order of preference)
a – still in the first bracha [Rav Chaim Kanievsky] (like if you came two seconds late)
b – still in the first 3 brachos
c – most of the SE has not yet been said [according to Rav Belsky], like if you came one minute late or something
d – ten people who started on time are still davening SE when you start
e – one person who started on time is still davening SE when you start [Chazon Ish, as confirmed by Rav Chaim Kanievsky shlita)
3) You have to stand with your feet together so that it looks like 1 foot, to resemble the malachim. B’dieved, this is not me’akev, and one who davened SE with his feet wide apart will not have to repeat SE.
4) The halacha is that your voice should not be audible to [any] other people besides yourself [when davening with a minyan]. Or at least try not to disturb other people, even if you do raise your voice somewhat. According to the Zohar, your voice should not be audible at all; you should just be forming the words with your lips.
5) Yes, say Kedusha with the chazzan and finish the third bracha (hakeil hakadosh) as well as “shomea tefilla” simultaneously with the chazzan. And bow at Modim.
6) It is preferable to stand for the entire duration of chazoras hashatz. This is not a full obligation (according to Rav Auerbach, it is a stringency), but it is the custom of bnei Torah to stand. If you don’t want to follow this, sit down after responding Amein to the bracha of hakeil hakadosh. Don’t sit before then.
7) Mashiv haruach – If you remember while you are still reciting the 2nd bracha, say it. If you remember before starting the 3rd bracha, say it. Otherwise, no good.
V’sein tal umatar – If you forgot to say it, then mention it during the bracha of Shema Koleinu before the words “Ki ata shomea…” If not, then say it after “shomea tefilla” before uttering the word “Retzei.” If you already uttered the word “Retzei,” go back to Barech aleinu. If you finished SE, repeat from the beginning.
Yaaleh v’yavo, if not said in its proper place [during the bracha of Retzei], can be said if you have not yet uttered the word “Modim.” If the word “Modim” was uttered, stop and return to the beginning of Retzei. If SE was finished, repeat from the beginning, unless it was Maariv of Rosh Chodesh or unless you already davened Mussaf on Rosh Chodesh, in which case Shacharis should not be repeated.
Generally speaking, in some cases, you need to repeat SE from the beginning (like when you forgot mashiv haruach and already began the 3rd bracha). In that case, stop davening where-ever you are. In other cases (like vsein tal umatar), it may not be necessary to go all the way back to the beginning.
8) Machlokes between Chayei Adam and Steipler Gaon – Chayei Adam says you cannot repeat a bracha of SE that you may possibly have already said. Therefore, continue from a bracha that you certainly did not say yet.
Steipler Gaon says all 19 brachos are me’akev one another. Therefore, all 19 brachos must be said even if you are possibly repeating something that you already said.
Other parts of davening – depends. What are you talking about here?
9) Stop your SE and listen with intent to be yotzi Kedusha. Machlokes if you need to listen to the verse beginning Yimloch. After hearing Kedusha [or at least the main parts of Kedusha – which are Kadosh… and Baruch…] keep davening. It is OK to continue davening in between the verses of Kedusha if you desire to do so.
10) Do you mean during chazoras hashatz? Nope. [Rav Chaim Kanievsky and others]