The correct answers are I leave my haunted mansion to whoever can spend a full night inside it. and I leave my vintage sports car to whomever my cat chooses to sit on.

In formal English, the choice between whoever and whomever depends entirely on its grammatical function inside the nominal relative clause, regardless of the clause's role in the main sentence.

In the first correct sentence, whoever is the subject of the verb phrase "can spend." Even though the whole clause is the object of the preposition "to," the subject pronoun is required.

In the second correct sentence, whomever is the object of the preposition "on" ("my cat chooses to sit on [whomever]").