b) a signed written document

I am not a lawyer and good for me for that. But I have had some law courses and I know that a) a valid offer and c) an exchange of something of value (sometimes called a consideration) and d) the parties entering into the contract must have the legal capacity to do so must be a part of all contracts.
Some states require that all real estate contracts be written, others just give preference. An oral contract is valid.

I apologize for the wrong answers.