1) is easy, most digital cameras can use AC adapters
2) batteries need to be removed because they get hot while charging and need to be open to the air to protect them from overheating
3) you will have to do the research re: mpeg video. Call Sony for this. 800.222.SONY
4) Unless you spend the money on a real video camera, you will not get less noisy video no matter what P&S camera you buy
5) The use of external mics are limited to proper video cameras, usually ones that cast in excess of $3,000