Nothing below is legal advice. I am not a lawyer. If law enforcement is actually requesting an encryption key, talk to a real lawyer.
To answer your first question, the answer is "the government probably can't demand the password, but might be able to demand the data." Some courts have ruled that the Fifth Amendment can prevent courts from forcing someone to decrypt data for the government, because the act of decrypting the data conveys information (see United States v. Doe from the 11th Circuit). Other courts have ruled that there are situations where that is not the case (US v. Fricosu, In re Boucher). Boucher is particularly interesting because the government first asked for the password itself, and then (when that subpoena was quashed by the magistrate) narrowed its request to the decrypted data on appeal. In the magistrate's opinion, we see
Also, the government
concedes that it cannot compel Boucher to disclose the
password to the grand jury because the disclosure would be
It is not generically a violation of the Fifth Amendment to compel production of documents (the 11th Circuit, quoting the Supreme Court, considered this a "settled proposition"). The issue is that the act of producing the documents can be considered testimony -- by producing the documents, the person is showing that they know the documents exist, where they are, how to read them, etc. Possession of the key to decrypt a file links you to that file, because keys are generally kept secret. In the 11th Circuit case, the court found that the government didn't know for a fact that a) Doe could decrypt the files, and b) what files existed on the encrypted drive. In the cases where forced decryption was allowed, the government had seen enough to independently show that the files existed, were authentic, and that the defendant had actual control/possession over them. The 11th Circuit asked for a bit more (the location), based on a standard that is in effect in some circuits but not others.
In any event, courts seem to generally consider this to take a court order to force production of anything; the police can't just order you to do it.