1) What is faster Nuclear propulsion, or modern day Diesel-Electric?
Nuclear, definately. All that I've read about have been able to outrun Diesel-Electrics
2) When submerged is Nuclear quieter or Modern day Electric?
Electric. Nuclear boats need essential systems to run the reactor to run at all times, silent running or not. With electrics, you can turn off all the systems without really risking the ship.
3) When surfaced is nuclear or Diesel quieter
This is a tough one. Nuclears bob and thrash alot on the surface, as they are designed to spend the majority of their patrol underwater. However, as is common knowledge, diesel engines, essential for recharging batteries, are very loud on the surface. On top of that, a D-E boat would spend more time ontop than a nuclear, so I'd give the nod to the Nukes.
Hope that helped