Yes, American football was originally based on the English rugby code. Over the years, the Americans continued to make alterations to the rules until the American version was essentially a completely different game.
No, not even close. AF is a stuttering, stop/start, play-by play game. There are offensive teams, defensive teams, special teams and kickers. Some players may only get literally 2 minutes of game time in a whole game. Rugby union is more flowing and all the players have to be fairly proficient at all facets of the game (bar kicking, which is a little more specialised).
American football can be traced back to rugby football, that is rugby came first.