You are welcome.
The square is public. I've seen taxis drive through the square, but I believe there are restrictions for private cars and cars that do not have any business there.
The only parts of the square that are restricted are along the buildings, you are to maintain a distance of a couple of meters or so, especially from the windows in the basement.
And around the guards themselves.
In contrast to the guardsmen at say the British palaces, the Danish Royal Lifeguardsmen are
not for show.
They have live rounds in the rifles and as such you are required to maintain a distance of about 1.5 meters or 5 feet from the guards.
In contrast to popular belief the guardsmen are allowed to both speak and look around - in fact that's their job. But they will naturally not do so unless there is a good reason.
Anyone, be they civillian or military including tourists are required by law to obey any order from a guard on duty.
It happens from time to time that the guards have to take action against people, usually intoxicated persons at night.
About 30 years or so back, there were a couple of instances where guardsmen fired warningshots against intruders at Fredensborg.
- I mention all this because I from time to time read about tourists who are confused when they are chased away when trying to pose next to a guardsmen at the royal palaces.