|1. A lot of still cameras shoot HD these days, so you could walk into JB Hi Fi and probably find one in your price range, but they won't be anything spectacular. Get what you pay for... so I can maybe lead you in the right direction, what's "Too expensive".
2. Set the camera up on a tripod, good video i something easy to watch, hand held stuff is annoying and you won't get the detail of the climb at all. Audio is a different story, because I assume you won't be buying a microphone you'll have to capture the audio with the inbuilt mic, it'll sound like shit regardless of anything you buy. The only real way to get decent audio is to buy an external mic and sync it properly. to make the in built mic better, see if you can change the setting to turn off auto Gain. Again, a cheap camera may not have this function. Worst case scenario, find your microphone and try and jerry rig some way of reducing wind noise.
3. iMovie is easy, simple and clean. Not sure what the new Windows Movie Maker is like, but when I last used it it's a piece of shit, but it's free and on most Windows computers. If you're more inclined to find "other" routes of acquiring programs, Sony Vegas for Windows or Final Cut Pro for Mac... both will take a bit of getting used to.
4. That's completely up to you. You could make a sweet montage of your trip from very little filming.
My suggestion would be to buy a GoPro HD Hero2, a helmet camera. It's small, waterproof, lightweight, shoots HD video, relatively cheap, can also take photos.