I got the very last question wrong about SSL...oops, at least now I know.
Yeah, just because the connection between you and the site is secure, it doesn't mean that it's the site you think it is.
I have SSL/https available on one of my personal websites, and I could put a fake Bank of America site on there, and it would authenticate as just fine. It's not authenticating as BofA, it's just authenticating as URL matching a known certificate. The fact that it would appear as "https://www.bankofamerica.com.mypersonaldomain.us" just means you have to look beyond the first ".com". Plus, there is a vulnerability that lets you spoof a browser into displaying a 'cut off' address. (I think it's been patched in all current browsers, but if you're using an unpatched IE6, I could make it LOOK like you actually are on "https://www.bankofamerica.com", when you're actually on a different domain.)
Two big giveaways: Banks will *NEVER* ask you for your full credit card number, PLUS the three digit code on the back, PLUS your full SSN. (I was seriously worried once when one of my banks did ask for the full CC# plus verification code, though. I had to call them to make sure their site hadn't been hijacked, and promptly complained about the insecurity of asking for both of those bits of info at the same time.) And a bank will generally not put a link to a 'deep' page in an email, they will link to their home page, and tell you in the email to use standard login methods. (Although, again, some are still not as security-conscious as they should be.)