A couple of simple question...
I've downloaded Zotero, and I've created a library for my bibliography. Is there any way to save my library, so that I could open it in another computer? Also, can I transfer my library with a flash drive, or is that unnecessary?
In most cases I'd recommend just using sync (i.e. option B) which is by far the most user-friendly option.
Yes, the name on them will be updated when you change your username.