The power to admit states is a power reserved to the federal government. Once allowed to join, the power to approve any combining of states, splitting of states, or changing the border of a state by a fraction of an inch is a power reserved to the federal government. Since the federal government approves every other change then the power to approve a state leaving altogether is certainly implied. Or, if you prefer, a power reserved to the states as expressed through a vote in Congress.
No it is not. Nowhere in the constitution is it written that the federal government was given the power by the states to prevent states from seceding. The federal govt also does not have the power to make a state from the land of an existing state. That is expressly forbidden in the constitution. The power to prevent secession is nowhere implied in the constitution. Quite the contrary. Had it been clearly stated that the federal government had the right to use military force to prevent a state from leaving, not a single state would have ratified the constitution.
They had just fought a bloody and long war to gain their independence. They were not eager to give that up