You can use the existing crank, just use the inner cr and get some bmx cr bolts.
I would take the freewheel off and then put a track cog on with a bb lockring and locktite. I have never done this but many very informative people from this forum swear by this.
Most of these questions and more are archived at this site.
Sweet ride!!!!
I have been looking for a frame with a 650 front wheel for a fixed project. I would go fixed and not ss. with a frame like that but good luck with whatever you decide.