ZZP's shift kit is fine, But all you really need is some 1/4 ID spacers. 2 1/2" long and 2 3/4" long for a medium shift kit. 2 3/4" and 2 1" for a hard shift kit. costs a total of 3 dollars.
The horn... Hard to say without seeing it. If theres no wiring harness to it then something there is messed from the previous owner and that'd be why they hard wired a button to it.
Do the other steering wheel buttons work? It's possible that the clock spring in the steering wheel needs to be replaced, that will cause the steering wheel to loose electrical connection with the car.