Is there a coat check or room to hang you coats?

Yes there are a ton of racks along with lockers it fills up but you can manage no problem

There are a lot of coat racks and cubbies

Yes

I didn't notice I had the baby stroller so I just put them under it

Yes. By the main entrance.

There are coat racks and locker rentals

Yes, there are coat racks or you can also rent a small locker

Yes! There is a large coat area with hangers for your coats.