Does someone know my (old) Apple ID password?
Q1: Yes, it looks like someone entered your Apple ID and password.  I don't think there's any other situation where this type of dialog would be triggered.

Q2: You did the right thing in immediately changing your password.  There's nothing you can do to get more info on who is using your ID, you did everything I would've suggested.  My only remaining advice would be to contact Apple, chat would probably be easiest, and let them know what happened.  It's also good to see that there was no malicious activity on your account, however, you probably want to watch it for purchases every few days.  

You mentioned the potential for malware or a key logger, that's quite possible.  Make sure you're checking your machines regularly for malware (I use Malwarebytes), especially if anyone is logging into your Apple account on a Windows machine.