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You are correct in your rulings. The batting of the ball by B in both situations is ignored by rule as to what caused the ball to go into the endzone, force. The batting by B is also not a foul due to the fact the ball had not yet hit the ground. After a fumble or backward pass touches the ground B could be guilty of illegal batting. So the ball was in the endzone due to A's backward pass and fumble in the two situations. In the first situation this results in a safety as it was A's endzone and in the second it results in a touchback as it was B's endzone.
In your first situation if A's backward pass went out-of-bounds at the 1 then it is A's ball there and we are ready for the next down.
Force 2-13
ART. 2 . . . Responsibility for forcing the ball from the field of play across a goal line is attributed to the player who carries, snaps, passes, fumbles or kicks the ball, unless a new force is applied to either a backward pass, kick or fumble that has been grounded.
ART. 3 . . . The muffing or batting of a pass, kick or fumble in flight is not considered a new force.
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