If they have just your address and password to the wallet, can they use the password to find out your private key from another computer?
First, forget about a thief using an address of yours to gain some advantage; in either of your examples or any other, having a bitcoin address doesn't benefit thieves.
Having the wallet password or a private key does benefit thieves. The private key works anywhere at any time, whether you're a thief or the owner, with no knowledge of anything about owner for it to work. So that's the most dangerous bit of information you could lose.
The password only works if you have a copy of (or access to) the relevant wallet file. So if someone has your password, knows it's yours, and know you, and can find you, your computer or your wallet file, then your funds are in danger.