The approach on AMVGuide involves converting your sources to editing-friendly formats; so it should pretty much cover everything you need if you follow it from start to finish:
http://amvguide.blogspot.ca/2012/08/introduction.html1. If you are asking about using the audio from a video file, see section 1.a, d.
Note: This method involves an understanding of script-serving your audio/video into VirtualDub-- which is connected to the rest of the guide.?? so it's best to read from the beginning. It's a bit awkward for beginners, but IMO, it still gives you the most control over your media. (So, learning how to do it is useful for all kinds of A/V manipulation too.)
2. See Section 2.III.(1)
3. That's a bit hard to answer since it depends on what you want to do; but I would say the cheapest *advisable* program that will still give you a sense of speed, reliability and precision would be Magix Movie Edit Pro, so that's what I've chosen to use in the tutorials for video-editing. Do note: I haven't kept up-to-date with the latest version, but it'll cost ~$50-$150
Otherwise, I've set up a poll for the most common software used in AMVs on the homepage here:
http://amvguide.blogspot.ca/ (See second post)
(I reset it recently, but here were the
2012 Software Poll Results)
Hope this helps.