Some trojans have more flexibility than others. So if the case is that you're infected with a trojan, there isn't really a way to tell how much can happen. But they can definitely make it look like you're doing things you're not. Or they could add files to your system, as well as remove them. You probably knew all that, though.
If you have reason to suspect someone has gained access to your system or someone is faking your IP address, first download and set up ZoneAlarm as previously suggested.
-RSI