Painting MDF crown moulding
1) It is very common to do one finish coat on the ground, and then a second on the wall.
2) If you have a real airless sprayer, go ahead and spray on the off-the-wall coat. But if the only sprayer you have is some hand-held gadget from BigBoxCo, use a quality brush instead.
3) I personally use Gloss Waterbourne ProClassic from Sherwin on my trim, but SWP sheens tend to run a little flat, so it might be between a semi and full gloss with other brands. Satin is somewhat flatter than most trim is usually painted. You can certainly paint with satin though. With trim, the main concern is usually durability and cleanability. This is obviously not an issue with crown.