Some improvements, questions and fixes

This PR contains a number of issues. Please feel free to comment what I should remove, I will make a PR which contains only the things you accept as contributions, so you do not need to hand-merge them.
Actually, I usually take the opposite perspective -- the sender can write whatever he wants, but we need to tell the receiver how to *interpret* it.  :)  Much like codecs are usually defined by their decoders [RFC6716].

In any case, the point is the JWK here is the key that the recipient of the message will use to verify the signature.  So how about "the key that should be used to verify" (just changing verb from yours)?