The correct answers are We are looking at a house whose roof is entirely made of pancake batter and Meet the landlord whose cats have their own dedicated bedrooms.

Whose is a possessive relative pronoun. Unlike who (which only refers to people), whose can be used to show possession for both animate beings (the landlord) and inanimate objects (the house).

Who's is a contraction for who is or who has; it cannot be used to show possession. Furthermore, "of which its" is redundant and grammatically incorrect; the proper phrasing would simply be "whose doors" or "the doors of which."