<< 1. Should I rip all of the old tiles up before putting down the new ones, or
install the new ones over top of the old? >>
Get rid of the old tile. All of its defects will show in the new tile.
<< 2. Can this be done without replacing the subfloor underneath? >>
Depends on the condition of the subfloor. Some sanding, levelling, renailing
may be needed to obtain a nice substrate. Bondo works well here.
<< 3. If I don't need to remove the subfloor, should I sand the floor before
installing the tiles? >>
See 2) above.
<< 4. I'm going to replace the tiles with self adhesive tiles, should I put
some kind of adhesive or primer on the floor before installing the tiles to
make sure they bond well? >>
Absolutely. Any cheap oil based primer or poly varnish works just fine.
<< 5. Do any of you know of a good website, or FAQ about installing vinyl
Most of what you need to know is on the boxes the tiles are packaged in. Check
out the DIY books at your box store and/or library for more info.