The coat of arms is quartered: the top left and bottom right quarters are the three lions [originally leopards] of England, the top right is the lion of Scotland; the bottom left is the harp of Ireland.
The lion on the crown is again the symbol for the King/Queen.
For precise information see here: Royal coat of arms of the United Kingdom - Wikipedia, the free encyclopedia
#3 It is not a must. The motto is old French and goes back to the days when French was the court language.