What is the proper way to patch acoustic ceiling after collecting possible asbestos sample?
My thoughts on your first question would be to take a sample from a few different rooms, if you can see any differences between color/texture on the ceilings. From asbestos.com: 


  If the material looks different
  (especially in color or texture) in
  different parts of the room, plan to
  sample each of those areas. For a
  ceiling surface in a large room, two
  samples may be needed to determine
  your asbestos situation. Try to
  balance the need to protect your
  family from exposure after you sample
  (to sample in an inconspicuous area)
  with the need to get a representative
  sample of the material (to sample in
  the center of the room).


I'm not sure about the size of sample required, but I don't think you'd need more than a few square inches. 

As for patching the ceiling, you should prime the sample spot before painting. After that, you can mix some standard ceiling paint with a texture additive to match the consistency of your original ceiling. Since it's a small area, you can probably get away with using a brush, or possibly a small roller. Or, instead of bothering with texture matching, you could go the easy route and use spray-on popcorn ceiling texture after priming (beware the horrible product reviews though - it might be easier to use a pre-mixed product).