1) yes, you need to be on a server that supports the latest version of WordPress before you upgrade - it won't work otherwise.
2) you'll login where you install it. I'm guessing you're planning on creating a network [codex.wordpress.org] and then mapping domains [wordpress.org]
3) The only way to answer this is to test your current theme against the latest version of WordPress. (you could create a copy of your site on a development server for testing)
4) backup everything before you even attempt the upgrade. Everthing means all files on the server plus a complete database backup.