What is the ruling of Islamic law on creating fake accounts with names of the opposite gender on Facebook to follow others' posts? Does the ruling differ if the purpose is to understand a girl's thinking for the purpose of proposing marriage?

It is not permissible for a man to pretend to be a female on social media to be able to view what women post, because that constitutes an aggression and an infringement upon what he has not been authorized to see.

As for a man accessing the account of a woman he intends to propose to, for a legitimate need, there is no harm in it, provided that it is limited to the extent of the need, and that he does not view anything that he is not permitted to see, such as immodest pictures and the like.