No.1: IE is probably your default web browser, so it comes up first when the URL is requested. In the Firefox Preferences (Main Tab), check the box "Always check to see if Firefox is the default browser", then restart it. Next time you start IE, it will complain that it's not the default any more - tell it No.
No. 2: Thunderbird can support anything that uses standard mail protocols: POP3/SMTP or IMAP. I have it set up for three different accounts at the moment: GMail (custom POP3), a POP3 mail account, and another IMAP mail account from my university. I've never used Hotmail, but according to
this guy, they don't give you any POP3 or IMAP options. Not Thunderbird's fault - Microshaft's.