1. There are heaps of Live CDs around. Every major distribution has a Live CD. Here's a few to look for:
All *buntu versions
Mandriva (look for Mandriva One)
Debian (might be "unofficial")
Slax (purely Live CD)
2. The first 6 I listed above will do the job for you. Try them all and see what you prefer. Some may work better on your hardware than others. Debian may be a bit tricky if you've never used Linux before.
3. Personal preference and hardware support. That's about all that separates them. All of them can be made into whatever you want them to.
4. You can try this program: http://etree.org/md5com.html
There's plenty of md5sum checking programs around, just Google for them. Also, since you're using Vista, make sure to check the "verify disc after burning" option when you write the ISO to a disc.