As far as the noise when the jack is plugged all the way in, I have a possible theory. Keep in mind this is pure conjecture because I don't know the exact configuration you have. So without further adieu...

The headphone jack comming out of the back of you amp is most likely stereo. This means its set up for a TRS (Tip-Ring-Sleeve) sheilded cable. The normal guitar cable is TS (Tip-Sleeve)

The Line In of the sound card is most assuredly of the TRS type.

Bottom Line, try using a sheilded stereo cable and see if it solves the problem. These cables are available at the rat shack.