1, Catholics believe in the Real Presence, many protestants do not. Ergo - it is inappropriate for them to take communion because they do not understand what they are doing.
Perhaps, but we should let God sort that out.
2, God has made it very clear that Communion should only be taken in a worthy manner. This applies to everyone.
Is His word not good enough for you?
No he hasn't, so no. Nowhere in the Bible does it say who can and can't have Communion, and even if it did, it would just be some silliness written down by a person and put into the Bible cannon for political reasons centuries later.