A website earns its cost by doing one specific job. Deciding what that job is takes an hour and saves most of the argument later.
It depends on scope, which is why no number is published here. You get a real quote in conversation once the scope is clear, rather than a range wide enough to be useless.
Yes. Plenty of engagements are a rebuild of specific parts rather than starting over, and that is usually cheaper and less risky.
You do, on final payment. It is in the contract.