As you said, squadron dependent.From the CS&D
220.127.116.11.4. Elevators. C4Cs will not use elevators under normal circumstances. C4Cs may use elevators when medically required, when moving objects that require an elevator with permission of an upper-class cadet, or for removing bulk items of trash.
I'd be surprised if your DD would have been prohibited from using the elevators if she asked. That being said, I'm sure some squadrons do stuff like that.
While Doolies are technically not allowed to have non-issued bedding, if you hypothetically put a mattress pad in your trunk every morning, I don't believe they can check there. Hypothetically, of course