(a) That's not my experience. This site of mine is secured with a StartCom cert, and Safari has always been perfectly happy with it: https://mappiness.me
(b) Why? I understood they were among the better providers.
Interesting, and a bit concerning. I just checked it on a friend's MacBook too, and that worked (Safari 6.0.5). Perhaps there's been a change at some point?
a) Well, if you setup your startcom SSL cert with the browser, that means you've been forced to add StartCOM to your truststores.
b) I simply don't trust them, particularly since they use a keybased auth system -- any compromised computer that was used to setup a startcom cert can download the private keys
b) I think it's moot whether this is better or worse than a password, but I'd probably pick the key-based system (which requires you to physically have my computer) over a password-based one (which might be hacked remotely).