That - to my understanding - is backwards. The power of the monarch is subordinated under Parliament. Parliamentary sovereignty is inherent, not derived from the crown.
HMG - not parliament - exercises the royal prerogative (those powers retained by the Crown) on behalf of the monarch.
In reality, yes. But technically the monarch can veto any Act of Parliament and appoint anyone as PM, though this would last about a day until there was a 'revolution' and the monarch was formally stripped of power.