What year is the bike?

700c wheels fit just fine

You'll need spacers for the rear hub, or you'll need to cold set the rear triangle down to 120mm.

Your crank/adapter will work but I'd recommend this adapter over the black ops unit for a more precise fit. Euro to American Bicycle Bottom Bracket Adapter - SILVER

Check with State, but I believe you'll need a 103mm BB for that crank, not a 110mm.

Check in the "Mechanics" or "Classic and Vintage" forums for info on the brakes.