Short, short answer: Yes.

If we start from the premise that your system has somehow been compromised (by a direct attack, inadvertently launching a malicious application, or whatever) then it's usually best to assume that anything you do on that system can be monitored or tampered with. As for detection and mitigation, it depends entirely on what the attacker is doing. If they got you to execute a run-of-the-mill trojan then you can probably just install a decent anti-virus app and go from there. If they're sitting upstream of your connection and messing with your traffic (unlikely), then things get more complicated.

Realistically, there are too many possible explanations for the stated behavior to draw any clear conclusions, and it's always possible that it's something benign (e.g. a overzealous spam filter). If you really think someone is in your system, the best course of action is pretty much always to back up your data, malware scan the hell out of it, burn the system to the ground, reinstall the OS and apps, update and patch everything, load your data from backup and make sure you're running a decent anti-virus product.

Also, make sure you're behind a firewall or router using NAT. That will keep most of the automated attacks that are constantly bombarding broadband connections at arms-length.
-xinc