why does the judge have to even acknowledge a request for an 80% bond discount? so trump can then ask for a 90% discount? so that every re-negotiation allows more delays?

Theoretically, there's no delays at all. New York is apparently a "no safe days" state, so that the state could theoretically execute the judgment at any time after it's been entered unless a stay has been imposed. A stay is automatically imposed without a hearing if a bond is posted and an appeal filed, so that's a safe harbor for Trump. My understanding is that although the rules of civil procedure don't provide for a delay in executing the judgment, the state has agreed that they won't do it for thirty days to give Trump the same amount of time he would have to secure a bond if this was in federal court.

As for considering the request, the rules of civil procedure also allow a court to enter a stay of the judgement (in whole or in part) pending appeal, separate from the automatic stay caused by a bond. Presumably, when a court has the power to grant a stay, there would be an implicit right of the party to: i) request that they do it (by appropriate motion); and ii) have an opportunity to argue that to the judge. Hence, today's hearing.

- i still have not seen an estimate of how much trump would be out, on a nonrefundable running total, for ~$0.5B bond.

The media reports have said that the typical premium for an appeal bond would be 1-3% of the face value of the judgment (including pre-judgment interest).