Is it normal for the medicine pack for a dry socket to fall out?

Yes. It is meant to fall out with time. If you are bleeding or having a problem, call the dentist or oral surgeon who performed or discuss with the doctor on call. Otherwise, observe and it should be okay. Do not hesitate to call or be seen. Socket to me!
Yes . It can happen. There are several types of medications that can be placed in a dry socket. Some are more prone to coming out by themselves.