my window is the same after I had the drivers door replaced. I will get round to adjusting it eventually.
In regards to the question, no the window doesn't drop. My Alfa GTV did, and I beleive BMW 3-series cabs do too, but not the Supra. Incidentally, wind noise was a problem from those windows on the Alfa, but the Supra is great.
Engine shouldn't idle above 800rpm once fully warmed up. If you don't let the engine calm down after the fast-idle period, it will still need time to relax its idle point even after long driving, but if yours is staying high full-stop then there's a problem.