yes, i agree that you should let your baby sleep in your room at night, because your puppy wants to be with his pack.
as for the separation anxiety. you can work with him on it. try telling him to wait while you leave the room, and close the door and leave him in your bedroom. and then open the door after a few seconds, reward and lots of praises. then tell him to wait again, and each time leave him in the room a bit longer, and reward him with treats and/or love.
this will allow your puppy to learn that you WILL return! and that it is ok for you to leave.
you don't have to use the word 'wait', you can use whatever word you want, but be consistent with it.
good luck!
