Remove trunk latch bolts with a long extension and socket and lift trunk! Bet they aint in there anyway, most of the time left somewhere else, should be able to see them with a flashlight through back seat opening.
Yep but still needs to charge the battery so that would be the best place to start and see if it really has to be on. I have seen some that do but worth trying first. Reckon it don't matter, evidently.
I have done that a bunch of times for folks and the keys are rarely in the trunk in fact never for the customers i have had! One lady found hers in her coat pocket hanging in the closet about a week later! Maybe you will find yours somewhere and if your luck is like mine after you have paid for another set.