Her Majesty requires no passport or driver licence. What about HRH the Prince?

The Queen is the only member of the Royal family who does not require a passport, a driving licence or car number plates. All the others have them. In the case of passports, the working Royals would have diplomatic passports. 

It is only the monarch who doesn't need licenses, passports, because the monarch is the one who issues them. All other royals must have these items.

These documents are issued in the Queen's name, everyone else has to have these, with no exceptions. 

This ONLY applies to The Queen.

Only applies to the monarch. Her official cars also do not require number plates. The Queen has never had to take the driving test either, but that applies to people her age who learned to drive before driving licences came in.

It’s only the monarch who is exempt from needing those documents.  They are issued by the government in her name.  The monarch can personally request admittance to another country when travel is for recreational or diplomatic purposes. 

Theoretically, at times when a monarch has travelled internationally with their spouse and children.  He or she can personally request that entry to another country be granted to the rest of the entourage, but whether or not they’ve done so I’m not sure.