Is a father's waiver of his house to his young children considered religiously invalid, and is it permissible to transfer ownership of the house to their names after his death, given that he paid part of its price before his death and wrote a waiver document and had it witnessed?

It is not permissible to favor some children over others in gifts unless there is a legitimate Sharia (definition)-compliant reason. What your father did by transferring ownership to you without including your siblings is impermissible and must be revoked, whether it was a void gift due to lack of equality, or a will for an heir which is only valid with the approval of the other heirs. Even according to those who do not mandate equality, the gift of a residential dwelling is only valid if it is vacated of its contents before the death illness; therefore, this gift is not valid under any circumstances.