Euroleague and NBA both generally have game results up the within the hour of a games completion. (at worst)
As in results or match reports? NBL have them up pretty quickly I think.
Ladder is often updated shortly after, though over the xmas break it was a bit crap. I suspect they have staff working typical hours when fans are often hitting the site outside of regular hours.
Can't speak for Plays of the Week, I rarely go to the NBL site. They should have them, yes. Perform provides the footage - ATF gets it up quickly.
Monthly awards seem to be announced on a Monday which can add a few days depending on when the voting due date is. The October email went out on November 1. Most recent one was a while after - maybe due to change over in staff?
The Sporting Pulse stats shit me. They're inexcusably bad IMO.