Why do I get sent to myspace whenever I try to log onto facebook?

sounds like you fell for a phishing attack, it's when hackers make fake pages to look like login screens of whatever website they want, then when u type in ur username and password it doesn't really log you in, cause it's not the real site you think you're logging on to, and your username and password are stored in a text file together for them to see and then they do what they want with ur account

I'm not sure if there is a specific 'was last on line'.. thingy but there is the little on line icon that tells people if you're on line but you can turn this off, also they can tell from the mini feed and other feed thingy. You can disable these too though so none of your information is on view to any one, not even your friends. I personally don't need everyone knowing every little thing so I disabled mine. It's under you security settings under profile I think.

sounds almost as if someone is trying to phish ur account passwords

Change your Facebook password IMMEDIATELY!

You could save your account if you change it quickly.

Clear your cookies and cached pages. That may help.