I believe that the good enging is a DX sedan and the bad engine is a EX coupe.
The DX will be an easy swap with the EX. If you use the EX wiring harness, I'm not sure exactly how many but you'll definitely have a loose connector that is for VTEC. I believe you'll also need to extend the primary o2 sensor wire since it's at a different location on the DX motor.The intake looks different.
Correct, axle back/muffler is the same.I don't think it effects the axle back.
That will be the simplest and easiest route.I would just use the DX motor with the EX exhaust set up.