Where could I set the username/password if the HTTP/HTTPS proxy requires it? Is Firefox securely storing the username/password?
Passwords and client SSL certificates are stored in database files like key3.db under your Firefox profile directory. Those passwords and certificates are secure (not stored as plain-text) if, and only if, you have a master password set in Firefox. You can set the master password under Preferences -> Security. Once a master password is set, you will need to enter it the first time Firefox attempt to access the secure store or attempts a SSL connection. You can also set a timeout, IIRC, for Firefox to forget the master password and it will ask next time it's needed. Without a master password, there is no way for Firefox to securely store something that only it/the user can see.