I have a question regarding these two figures' special powers:

For The Bat-Man it's:

THE HOUSE ALWAYS WINS: Immediately before The Bat-Man makes an attack roll, you may choose a number between 1 and 6. If the attack hits and the chosen number is on one die, modify his damage value by +1. If the attack hits and chosen number is on both dice, instead modify his damage value by +2, and after actions resolve, heal The Bat-Man of 2 damage.

And for The Riddler it's:

RIDDLE ME THIS: The Riddler can use Incapacitate. He can use it normally or as a free action targeting a single opposing character if he has been given and will take no other free actions that turn. When he uses Incapacitate as a free action, and successfully hits a target, choose a number from 1 to 6 and roll 2d6. If the chosen number comes up on either die, Incapacitate resolves normally; if the chosen number comes up on both die, give the target 2 action tokens if it has zero action tokens.

Now, I believe according to NBPerp, if, when using the Riddler's special power, the number you pick doesn't come up on either die, then no action tokens are given. The Incap attack is said to have hit, but no tokens are given.

Does that mean when The Bat-Man uses his special ability and the number you pick doesn't come up on either die, he does no damage? Meaning that the attack is considered "a hit", but deals damage of 0?

Seems to me, that would be a valid way to view this. There is nothing explicit in The Riddler's power that says no action token is given if the number does not appear on either die. Obviously there's nothing in The Bat-Man's power description that says if the number does not appear, then damage dealt is zero. But in using The Riddler as precedent, I think you can make the argument.

If Bat-Man's damage value were being replaced I think you would be correct, but since the damage value is being modified, if the chosen number isn't rolled, you would just deal the printed damage value.

If Riddler rolls the chosen number on one die, Incapacitate resolves normally - therefore it is implied that if the chosen number is not rolled, Inåpacitate does not resolve normally. The Bat-man has no such clause though, so the effects from The House always wins is in addition to the normal effects of the attack, not instead of them.