Can you take R-22 out of the old compresser that is not working and put it in the new compresser? Or does this mess up the compresser when using recycaled R-22?

If you had a compressor failure, the refrigerant reclaimed from the system should Definitely not be reused ever any where. Refrigerant can be reclaimed and reused if the system it was reclaimed from was in perfect working condition. Also, if compressor failed, make sure dryer filter is replaced at same time as compressor. Then start from scratch with vacuum and new refrigerent.