I don't know what Opera's email client is like because they came out with it after I switched to IMAP and it doesn't support IMAP. My advice is perhaps find another email client? I normally use Eudora - there may be a Mac version of that.
As to the Banks thing: firstly, email them and ask them what you can do to convince them to retool their web pages with proper, compliant HTML. Mention that you are using Opera because it's better than IE and NS6. And at least as compliane as IE. Secondly, try setting Opera's agent string to IE. That also enables a few more Javascript objects for code expecting IE, although it doesn't enable faulty Javascript code.
Wade.