re: How does Trump’s half billon dollar bond in NY not violate the 8th amendment?

It's not bail, it's an appeal bond, which is standard in civil cases. Trump doesn't have to post the bond, but if he doesn't then New York can start collecting on the judgment.

The 8th Amendment arguments may be raised against the judgment, but not the bond.

Thus was a civil case, though, and the 8th Amendment does not apply to civil damages. To the extent the damages were punitive in nature, the 8th Amendment might apply, but it's not clear.

Trumps better argument is the massive damage award violates due process.