How should I be using keychain access?

Hi, I am very new to macs. I've never used OSX before about a week ago, but I am picking up on it well (I've used GNU/Linux for almost ten years so I know my way around an operating system).

But I don't really think keychain access is working as it should...It's hard to explain. I mean, the way I understand it, shouldn't it be saving the passwords I type into Safari and auto-filling them? Because it only auto-fills some passwords. Paypal autofills, but my bank's website doesn't, and even this forum doesn't autofill. I have to type in my password every time I visit.

Is this working as intended? Is there a way I can get Safari or Keychain to fill in all passwords for me automatically?

This is leopard on an iMac G5 iSight model. I did a fresh install like a week ago.

Sorry if my question is vague but that's the best I can do with the amount I understand.