Paintballs are filled with a water-soluble dye. It is easily washable, but stubborn stains can occur when the 'paint' has penetrated deeper into the fibers. I think that Sheldon wanted to make sure that not one microscopic mark is left on or in the cushion.

I guess, for the official cleaners. But I didn't think it made sense that they wouldn't have had better results with what Leonard and Penny were doing first. It looked to me more like they actually made it worse by spreading the stuff around. Regular cleaning should have done better. But of course, it couldn't, Because Plot.

Sheldon trusting Leonard or Penny to clean anything.

Ultimately, yes. But I still think the "stain" should have been a lot less by the time Sheldon saw it.

The dry cleaner must have done an excellent job. Instead of throwing the cushion away or burning it, when Howard sat on it, he went there again.

Eh, don't give them too much credit. Maybe they just wanted to have someone say "astronaut genitalia."