all the dogs i have ever owned or known have had nightmares. my current dog is 2.5 and he has nightmares every night although not as severe as you describe. they are mostly him twitching loads, growling (he has never growled whilst awake!), whimpering and small barks. his heartrate also gets very fast for around 15-30 seconds during the most animated parts of his dreams.
i'm sure your puppy is perfectly normal and is probably still in transition stage, getting used to his new life without his mother and siblings and his new home, new family members. if you are worried about him you could give the vet a ring and ask but i think he sounds normal.
Mine is the same age and she's having nightmares too. I seem to remember previous puppies dreaming very vividly, lots of running movements and yipping but this one really screams out and wakes herself up. She's a very nervous puppy and this has been an eventful week as she's now allowed out walking so I think she is processing all the new stuff that's happened.