How does a penalty affect first and goal?

Answer 1

If the penalty is assessed against the defense, the ball will be moved that number of yards toward the goal, or half the distance to the goal, whichever is less. the same applies in the opposite direction, except that it's highly unlikely that half the distance to the goal behind you will ever be less than the penalty yardage unless there are a lot of consecutive penalties on first down or the QB is an idiot and runs the wrong way before getting penalized. In any case, a dead-ball foul will cause first-down to be replayed with the modified yardage to go (usually 5 or 15, but depends on the penalty assessed).