#1. It should indicate where the login attempt was coming from. I havent had anyone try to access my account because my password is too cumbersome for anyone to remember! =) Oh, I'm using a Macbook, so Im pretty much safe from any viruses or <anything>ware that could spy on my typing (keyloggers) etc.
#2. I've had many of those. I just "remove" them and move on. I get many requests from shady women which I always decline then mark as spam so they dont bother me.
#3. I will give you a free tip that I give to everyone else with Facebook problems. It would protect you against would be spammers/hackers from copying your profile and then friend requesting them, etc. then push "lottery" or flirt them up, etc.
Simple, go to your timeline, then click Friends, then click the pencil icon next to Find Friends, then click Edit Privacy. Make sure all the options are set to ONLY ME. That way no one can see your friends list but you, with exception of mutual friends.
I've had my profile copied a few years ago, and someone alerted me. I just did the steps above. No problems ever since!