3_Yes it should handle it fine on that res
Only half correct.
At 1024x768, I would say Yes.
At 1280x1024, I would say No.
It would help if the OP explained what he means by "full settings" and "handle" as this can be a combination of several things including graphics settings included with the game, and/or also including AA and AF. With No AA, you might be decent, but that depends on your definition of "handle". It won't be 60 fps.
In response to the first question about jittering, check your PSU's ratings. Its possible that the entire system isn't getting enough juice when it is put at load. While both the CPU and GPU are relatively efficient, if you've got a weak PSU this could be the issue. Also, it could be driver related, usually graphics or sound, so check those out.