Player A uses Defender's enhance on their throw attack with the other card in their card pool being a non-attack. Both players skip the rest of their enhances. Player B completely blocks Player A's attack and responds with Feline Grace. Since the block is checked during the block step and the damage step hasn't been reached yet, is the throw attack is added to momentum before the damage step resolves? And if so, does it deal damage during the damage step or does the damage step get skipped because there is no attack to resolve anymore?

Because the attack has made it to the Block Step, the attack will finish resolving, including dealing damage, if applicable (see ***Donovan*** vs. BRT + Dark Heart during the Block Step).

As for the attack, yes, it will be added to the momentum before the Damage Step.

As a note, the quality of the block is checked after the block step but before damage is actually dealt, so yes, Feline Grace can add the attack to the opponent's momentum. Defender will still resolve and let them add another card to their hand though.

edit: attacks only abort if they leave the card pool during their enhance step .