Am I entitled to claim the inheritance after the death of my grandfather, who passed away after my mother, especially given that my grandfather had written a monthly rental contract for an apartment to my mother, and not a deed of ownership?

You have no share in your grandfather's inheritance because a daughter's son is not an heir in the first place, and your mother died before him, and the dead do not inherit.

As for the apartment lease contract for an unknown period, it is an invalid contract.