1) Sometimes you can correct this by turning the TV on and off quickly a few times. Usually TVs have an automatic degaussing feature that works the first few seconds it's on. If they doesn't work I would suggest looking for a small electronic magnet (like a video tape eraser). You can get one off ebay for less than $20s. Barring that I would try a large speaker magnet or some active (i.e. turned on) vacuums cleaners can be used for this (but these are the least effective ways).

Usually adjusting the picture requires a bit of magic so you'll need to experiment with magnet placement and movement until you get it just right.

2. I would suggest just getting a simple audio mixer or switch. You might need to get some connectors to convert mini to RCA for the mixer. You should be able to find something pretty cheap at RadioShack or Fry's.