No. You cannot be compelled to consent.
I would say no. There's just nothing good that can come out of it. If you give police permission to begin rifling through your things, they might not necessarily find what they're looking for, but they might find something else that can cause problems for you. This is the concept of plain view. If the police see something that shouldn't be there and they otherwise have a right based on your consent to be there, they can take it and separately act on it.