1. Yes.
2. No. Buy a BMX freewheel, and then respace and redish the wheel. A SS kit is for a cassette type (or freehub) hub, and you have a freewheel hub. Look up both freewheel and freehub on Sheldon's site and you'll get the idea.
3. Probably a good idea to get a new chain too. And respace/redish, of course.