You have lots of questions in there...lol. I was surprised that the noise outside was even an issue!
This might be a good place to start with some noise reduction. I'd try some rubber feet under the motor to cut down on some of the vibration noise.
Yea, the cleaning part baffles me as well. He could have left that in the shop if that's what he was going to do!
The foam looks like insulation sheets to me
Yes, the 3/4 would cause more noise reduction but, come with a weight cost.
Paint - I'd start with a marine ply first if you're going this route. From there, the same paint you used on your house.
Bill Pentz is the "go to" source on DC!