If the Monarch went on a killing spree there is literally no legal recourse.
This is true of almost all heads of state.
The Freedom of Information Act exempts the entire Royal Family - why is this do you suppose
It doesn't. There is no exemption for the Royal Family in the Freedom of Information Act. They have the same exemption as every other citizen of the UK, including you and me. The Act applies to information held by public authorities. The Queen is not a public authority, nor is any other member of the Royal Family.
I doubt a GDPR submission to the Royal Family would be filled, and now we have left the EU there is no appeal to any court that could enforce it.
You would be wrong. Requests are dealt with by the Royal Family's Information Assurance team. If you have concerns, you can go to the ICO.
The Royal Household is exempt from things like the Equalities Act, their wills are sealed (nobody else's will is sealed), they are exempt from tax...the list just goes on and on (and on).
Again, much of this is standard for a Head of State. And other people's wills are sealed. It is unusual but the executors of any will can apply for the will to be sealed. To succeed, they must convince the court that it is undesirable or inappropriate for the will to be open to inspection.