Remember, in snooker, the black ball has no special connotation other than it being worth 7 points.
You have all basically presented the same scenario - that is, the frame ending in a draw.
- Black ball is the only ball remaining in play
- There is a difference of 7 points between players
- The player ahead by 7 commits a foul by pocketing the white ball in-off
- Black ball remains on the table
Assuming you aren't playing an "aggregate match", it's pretty straight forward...
The black ball is spotted, players draw lots for choice of playing next, first player starts with white ball in-hand, and the next score or foul ends the frame.
This is outlined in section 4 of the WPBSA official snooker rules:
4. End of Frame, Game, or Match
(a) When Black is the only object ball remaining on the table, the first score or foul ends the frame excepting only if the following conditions both apply:
- (i) the scores are then equal; and
- (ii) aggregate scores are not relevant.
(b) When both conditions in (a) above apply:
- (i) the Black is spotted;
- (ii) the players draw lots for choice of playing next;
- (iii) the next player plays from in-hand; and
- (iv) the next score or foul ends the frame
However, if the players had the same scores (tied) with only the black ball remaining, and player A scratched, it would be a loss of frame for that player.
Here is Ronnie O'Sullivan scratching on the black while tied with Xiao Guodong during the International Championship 2016. He scratches on the black ball resulting in loss of the frame.