Can you take your phone to record? I'm not asking because I want to use it during the flight, but if someone else could record while they wait for their turn?

Someone can record if they are not going to fly. You can't have anything inside the flying area.

Yes I've seen people doing it

I'm not sure. But they take stills and video for you to purchase. They are better quality than you could do with a phone. We bought ours and they aren't very pricey.

I'm pretty sure you can't. We locked all our personal effects in lockers.