Running is considered undignified unless you are being pursued by a dragon or other foul fiend. FNN shows documentaries about life on other planets, mainly Earth so the Kingdom can indulge in its favourite hobby of sneering at humanity and things like athletics are considered by the fairy world as humans showing off when they should be taking better care of their planet.
Transportation is by foot, wing, boot power (in the case of sprites), instant transportation spell (with the risk you may not rematerialize in the same order you disappeared in or at all!) or by using the cherry transporter trees. These are slower but safer. Entry is via the trunk via a special lever and inside the tree are abacuses used to set the co-ordinates for wherever you want to visit. From the outside the trees do not appear to move. The action takes place inside the trunk. The magic that propels them is conducted via the roots and branches. The Kingdom plants receptive cherry tree transporters on whatever world they visit, hence the one at Brenebourne. But not all areas in the Kingdom can take cherry trees, especially those places made barren by magical fighting so the instant transport charm must be used too. Hanastrew hates it, she tends to land in lakes, but Eileen is expert at all forms of magical transport as is the Queen.
There isn’t anything like a police force in the Kingdom. The nearest thing is the fairy squad, set up by Eileen, and now run by Hanastrew. It is expected each group will do its utmost to keep their own in line. This works reasonably well as nobody wants the fairy squad turning up and acting in what they’d consider was a heavy handed manner. The fairy squad isn’t known for subtlety. The overall authority is the Queen of course and nobody wants her acting in a heavy handed manner either as she could let all hell loose magically speaking. Crime rates are relatively low but, sadly, when it takes place it tends to be “spectacular”. For example Brankaresh murdered rivals to steal their spells and overthrew the Queen briefly and the Witch deliberately let a dragon loose to cause as much devastation as possible.
Village settlements tend to be well run - nobody wants to rock the boat and upset the neighbours.