Do the teams that win their divisions (and automatically get the top 3 seeds) automatically have homecourt advantage (even if the team they're playing has a better record)? Or could the sixth seed conceivably have homecourt advantage against the third seed in the first round?

it all goes by record. The only time that really matters according to rankings is between the 1 and 2 seeds, they are split by winners of the division then after that it doesnt matter. Team with a better record has home court.

Home court goes by record, but winners of each division get top 3 seeds, which affects who plays whom. So, could the Knicks win the Atlantic and still not get homecourt advantage? Sure. If playoffs started today, NY would be away against Washington, the 6 seed.

What I'm not sure of is whether they set the playoff "brackets" right before the playoffs start and keep them, or reset them based on records of surviving teams. Think it's the former -- So if NY wins w/ 3rd seed, they'd play winner of the 2nd seed vs. 7th seed, regardless of records of surviving teams. This right?

here's the scoop. HC is decided by record alone. Who you play is decided by what seed you are. Regardless of who wins you dont "reseed" in the NBA. It goes by brackets. The 1/8 winner plays the 4/5 winner and the 2/7 winner plays the 3/6 winner.

Yeah, thanks for clearing that up. I thought top four seeds had home court advantage for the 1st round.
Now that that's settled, we'll know we'll be getting homecourt advantage only because we have a better record.