Hat
Even though the movie was set in Boston, Jack Nicholson didn't want to wear the cap for the Boston Red Sox, so he wore his own NY Yankees cap.
Nowadays, probably a baseball cap. It used to be a "sombrero".
The person who answered before said 'baseball cap' but baseball is not a British game. It is a Cricket Cap. Cricket is a game played in the UK.
NY Mets
the best way to fit a baseball cap, especially an MLB game-hat which are difficult, you have to shower with the cap, saturating it. Then stretch it a bit, let it drip dry for about an hour, then wear it while still wet until completely dry.
no, you can wear anything you want, as long as your not impersonating a cop or claiming to have police powers.
New York Mets
Detroit Tigers
The types of caps that truck drivers wear slightly resembles a baseball cap. The section above the cap's bill is made of foam, whereas the back half of the hat is made of plastic mesh for breathability.
The cap badge of the British Parachute Regiment is relatively new as paratroopers did not exist until WW2. So it is a new design that has no historical tradition as common with many of the British regiments. One source I have says the badge was approved in May 1943. The badge is a simple design of Wings with a parachute in the center; the parachute being topped by a King's Crown and a Lion on top of the crown. It has a silver finish.
The winged horse Pegasus, the cap badge is wings eithrer side of a parachute.