April is Worlds (All Star cheer), minimum age to compete is 12, some are in their 30's. They are teenagers and young adults who travel from all over the world to compete. Because it is a very expensive competition, in addition to travel costs, not all kids are accompanied by a parent. You might have just their coaches and one or two parents per team. POP Warner (recreational/sideline cheer) are kids, mostly 14 and under with nearly all kids having a parent present.
Yes, cheerleaders stunt everywhere!

Yes, they dress in Nike Pros and Sports bras almost everywhere they go. My daughter lives in hers. Although, usually in the mall she might have a t-shirt over her sports bra. I often stop and run errands and it is very common and no issue for our cheerleader daughters to accompany us into publix, etc. in just Nike Pros and t-shirts. Nothing inappropriate about it. I suppose if you live in colder states you will not see it as often. As we live in Florida, no one pays it any attention here. You have people on their way to/from the beach, waterpark, etc. and stop into stores in beachwear.