30F in coop should be just fine for healthy 9 week olds.
My guess is they won't touch the plate (especially if it's hot) but I don't use any heat sources once chicks are moved into the coop (but different climate too of course).
Have they ever used the plate while inside the coop space before (that is to say, do they know it's there?) Probably wouldn't hurt to leave it on brooder setting, if that doesn't get too hot, in case they want it.
Well at least they're going in as it gets dark, so they're sensible enough to do that.
Iffy on that (also I don't get those types of temperatures). On one hand they should be feathered enough to do okay in those temps, on the other it's probably nervewracking to worry over if they'll do okay...
I'd let them decide, as long as they're willing to go in and out of the coop during day time as needed for shelter (sometimes chicks/young birds won't).