I think a 'no ball' is much more like a baseball 'ball' (a ball pitched not in the strike zone) in that it is a bowler/pitcher error. A foul ball is a ball hit into a none playing area (behind the batter) and is a error by the batter. Their is no foul area in cricket and this sort of error by a batsman ( letting the ball hit the bat and glance backwards) can result in an out if the ball is caught by the slips.
There are several mistakes than can result in the batting side getting extra runs.
A wide - a ball bowled way off target (there are two 'strike zones' in cricket: the small wicket, which if hit results in the batsman being 'bowled out' and a wider zone, basically the area that the batsman can reach with his bat at full stretch, which if missed results in a wide and a run being given to the batting side)
A bye - a run scored because of a fielding error where the ball is not hit but the fielding side don't stop the ball before the batsman makes a run (a tiny bit like a stolen base)
These runs scored because of bowling or fielding errors are not give to the batsman individual score but added as 'extras' to the batting sides score. Fast bowlers who run at speed before releasing the ball can often make mistakes, but are also sometimes very effective when on target, so you get the situation where extras are the largest single part of the score for the batting side.

Is all this british culture getting to much in culturally challenge Arkansas?