Will sleeping on a soft mattress affect my baby's growth? Eg. The bones formation.

Not likely... Babies in general move quite a bit during sleep..Soft/firm/pillow top beds probably won't make much of a difference since a new baby is only a few pound anyway. Just make sure baby sleeps on his/her back and that no blanket/bedding near face which may suffocate baby. Follow up with family doc/pediatrician regularly and ask lots of questions. Baby is precious. Congrats and good luck.