An answer to your first question:
In the 1800's there were many games named "football" that had differing rules in differing cities.
There were Rugby rules, Austrailian rules, American Rules, and Cambridge rules.
The Cambridge rules was the most popular in the British commonwealth because the game was more established, and how people couldn't get hurt as easily as when they played the Rugby rules.
The Rugby rules game went over to the USA and Austrailia.
Those countries liked the rules a lot but thought the game was unstructured. Pretty much like a mosh pit with a ball.
The Americans introduced end zones, play formations and stoppage of play every time a player was down, and the forward pass to make the game into a game of extreme strategy, a game that would challenge the minds of the college students that played the game at the time.
The familliar helmet and pads were only invented after the American players started to die after playing the game and President Theodore Roosevelt threatened to ban the game unless there were some saftey measures.
The Aussies got bored with rugby and decided to make their own game too.
But the Cambridge rules were far more associated with the name "Football" and the name stuck internationally as the game became popular.
That's why we call gridiron football "football".