The king is responsible to the barons. If the barons band together then the whole country (probably except the capital) is against the king.

The king is permitted to rule, as long as his rule is beneficial to the barons and the people.

Yes, the king can appoint barons. It is a big deal. It usually means deposing an existing baron and giving away their responsibilities / estates.

It is implicit in the role of monarch that if the king is shitty that they are deposed, removed or murdered because an actual popular resolution is fantastically destructive. See the French revolution.