I'll do my best to answer the clutch question.
Consider your kart with its large tires as something that requires this belt drive assembly. It is a torque converter and due to your large tires your gear ratio would be very out of whack with just a centrifugal chain drive clutch running to your main sprocket on the axle.
If you were to go to that drive set-up it would be similar to starting off a standard shift car in 4th gear. You wouldn't enjoy the outcome.
Regarding your light question if you still have the Tecumseh engine mounted on the kart you could track down an alternator or get a battery. With wiring I can't answer that question nor can anyone else, you have no plan. Without a set plan its hard to say, but typically you have 2 wires that go to lights one positive power wire, and one grounding wire. You'll want to interrupt the flow of current and guide it through a fuse and a switch, you can wire these at your convenience. If you're not sure what that means please use youtube to your advantage as there are several very good diy posters there regarding switches.
If you have further questions please lay them out in a better format with pictures to illustrate your query.
