If you are talking casually about a school that has a longer formal name, then no, you would not capitalize. It's possible that there is a club or restaurant somewhere named "The University", in which case you would capitalize.
No, except at the beginning of a sentence because it is n ot a proper n ou n.
Yes, becauseit is a proper n ou n. Example: Lourdes School of Makati Harvard University
Vanderbilt University, all of the Ivy League Schools and there are many, many more!
use I or a name of a town
no, university would be exactly as the word school or chair or table. eg: what university will he attend? as to : he is planning to go to the University of Manitoba.
Yes. 'Sun' is its name and you capitalize it just as you capitalize anyone's name.
Yes. It is Jane Doe, M.A., Ph.D. (Note the lower case h in Ph.D.)
If its a name.
You capitalize Apollo because it is a name.
No, but you capitalize the name of a biome.
I can name one at least: Ryerson University in Toronto, Ontario