Do I have a virus? My Mac is acting very strangely

Sounds like someone has downloaded a KEYLOGGER.

Sounds like it might be related to this. http://support.apple.com/kb/TS4135. Follow the steps in that article first to see if it resolves the issues.

If you think that someone had access to your computer and may have installed or added something... you should erase and reinstall as you suggested... selectively migrating documents and data from a backup afterwards.

You say someone "hacked in." Did this person have unmonitored physical access to your machine? If so, you should immediately erase the hard drive and reinstall a fresh system:

How to reinstall Mac OS X from scratch

If not, you probably don't have anything to worry about... at least, in regards to hacking. All the problems you describe could easily be the result of a hardware issue, so it would be a good idea to get the machine checked out by Apple.

One thing you can test beforehand, though... restart the machine in safe mode. If the problems persist in safe mode, it's definitely hardware. (Be sure you test in safe mode long enough to know whether the problems are truly gone or just haven't happened yet.) If they go away, and come back when you restart normally, then I'm wrong and it's a third-party software issue.

Donald Morgan wrote:

Sounds like someone has downloaded a KEYLOGGER.

Based on what? None of the reported symptoms give any indication that a keylogger is installed?

If you know or suspect that a hostile intruder has either had physical access to your computer, or has been able to log in remotely, then there are some steps you should take to make sure that the computer is safe to use.

First, if there's any chance that the incident will be the subject of legal action, then you should do nothing at all without consulting a lawyer or the police. Your computer would be the principal evidence in such a case, and you don't want to tamper with it.

Running any kind of software to scan for "viruses" or "rootkits" is worse than useless. If I broke into your system and wanted to leave a back door, I could do it in a way that would be undetectable by those means — and I don't pretend to any special skill as a hacker. You have to assume that any intruder could do whatever I could do. The "anti-virus" software itself will slow down and destabilize the computer with no offsetting benefit.

The only way you can be sure that the computer is not compromised is to erase at least the startup volume and restore it to something like the status quo ante. The easiest approach is to recover your entire system from a backup that predates the attack. Obviously, that's only practical if you know when the attack took place, and it was recent, and you have such a backup. You will lose all changes to your data, such as email, that were made after the time of the snapshot. Some of those changes can be restored from a later backup.

If you don't know when the attack happened, or if it was too long ago for a complete rollback to be feasible, then you should erase and install OS X. If you don't already have at least two complete, independent backups of your data, then you must make them first. One backup is not enough to be safe.

When you reboot after the installation, you'll be prompted to go through the initial setup process for a new computer. That’s when you transfer the data from one of your backups in Setup Assistant.

Select only users in the Setup Assistant dialog — not Applications, Other files and folders, or Computer & Network Settings. Don't transfer the Guest account, if it was enabled.

Reinstall your third-party software from original media or fresh downloads — not from a backup, which may be contaminated.