Lost Items and More

Hello, I have several questions on different topics. 1: Is it permissible to wear a short shirt and the like, as I saw in the Mishnah that it is written that one can wear from the hand to the elbow. 2: What is meant by "not to wear from the head down, as it causes forgetfulness," but there are things that cannot be avoided, such as T-shirts. 3: I lost a civics book, but then I saw a book that had been lying for several days on a table in the yeshiva (near where my class learns), and I am quite sure it is mine because I did not find mine, and I waited a few days and saw that no one took it, and I posted a sign in the yeshiva that if someone lost a civics book, they should tell me, but no one approached me (and it has a slight tear that I think, but am not sure, mine also had), am I allowed to take it, as it seems to be mine?! 4: I lost a simple round Casio watch, and then I noticed that there is one like it in an open compartment in the Beit Midrash near a bench in the Beit Midrash, and I study there a lot every day or at least most days, and I think it is mine because sometimes I take it off my hand and might have forgotten it on the table, and someone put it in that open compartment next to it, can I take it (I will just note that I waited a few days and saw that no one took it from there, it remained there)?

Hello and blessings 

1. One should wear a long shirt up to the elbow. 

2. I have not seen it written not to wear from the head, and on the contrary, it is written in the Shulchan Aruch (Orach Chaim, Siman 2, Seif 1) that this is how one wears clothing. 

3. It is probably yours. 

4. You can take it and announce for a few days, if someone else thinks it is theirs.