Don't put him on his stomach for napping nor for bedtime!!!!! Because of SIDS, Sudden Infant Death Syndrome. He can be on his tummy for tummy time, when he's awake and when you're there to watch him. I think it's normal that he's moving about when awake and sounds like a very active boy....great. I'm concerned about him do that when he's sleeping. My two older boys, 3 yo and 2yo did a little bit of jumping in their sleep, mostly in the beginning of their sleep, but I have not seen it happening with them in a long, long time and my third boy, he's 5 mos and he doesn't do that in his sleep. You should bring that up to the pediatrician about him doing that in his sleep. It's normal for them to hurt themselves from being so active with his arms, but I don't know what to say about him doing that in his sleep. PLEASE check with the pediatrician. Be careful with blankets in his crib and again, no laying him on his tummy when to sleep. He will cry when tummy time, they hate that, but just keep doing it about two times a day, few minutes here and there and add minutes after awhile and that is good for building strength in the neck, back and arms and so forth and rolling over he will do from tummy time. That is why you need to be careful about blanket especially when rolling over,he will find a way to get his arms out of from underneath the blankets. Be greatful that he's active, but talk with the pediatrician about the night one. Let us know how you turned out and what the pediatrician said about that. IF you are not satisfied with their response and feel something is wrong, speak up and advocate for him and get another opinion and another one if you haveto.