Looks like a basic coaster brake that can be removed. Though I'd advise adding a rim brake to the bike if you're using the frame the wheel came off of.
A caliper brake, cable and a brake lever. You can just take out the clutch from the coaster, there may be loose bearings in there or they may be caged.
I'd be inclined to remove all the guts and use a sealed bearing. They can be had in just about every size, going that route you will need a crush sleeve for you axle to run through.
Here, this will refresh you on a coaster brake.