Is it ok to let baby sleep in the bouncer all night ? does this hurt his back?

Yes and No: Yes and no. It is ok early, but the longer you allow this habit to entrench, when the baby is too big and needs the crib, transition may be difficult. The earkier the crib the easier. And no, it does not hurt the back.

Not the best: I worry more about the positional deformities that can result from sleeping in a swing/bouncer. Babies necks are not strong enough to reposition themselves, so when they are put to sleep in an upright posture, their heads drop to one side, and remain there until you move them. This can cause a tight neck muscle (torticollis) and flattening of the skull (plagiocephaly). Better to sleep in crib.