"Pinatutulog" and "pinapatulog" just mean the same thing. That is true for other pa-in, pa-an, and pag-an verbs. Since the standard rule for the present/uncompleted conjugation is to repeat the first syllable (or part of it) of the root word, "pinatutulog" should be the corresponding standard form. However, based on usage, I think one form is just as popular as the other.
I don't think so. I've been hearing both forms even from older people ever since. Possibly it's a regional variation. That some might find one form easier to pronounce than the other could have also been a factor.