I have quite a bit of experience with dance studios so perhaps my thoughts will help. My mother owned and directed a dance studio for 20+ years. I "grew up" there, spending most afternoons at the studio, either in class or, as I got older, helping run the studio and teaching. My daughter and I both have danced in several studio environments. I've observed dance studios from the parent, student, and instructor perspectives.
A professionally run, proper dance studio will require ballet students to wear a leotard, tights, and ballet shoes. They may or may not have requirements about how to wear the hair (usually less so at age 7). Most studios do not want or allow children who are potty trained and older to wear undies under the dancewear. It really isn't necessary, and bunched up undies can become a distraction for the dancer. As a teacher, I have had students in summer classes complain about tights being too hot. But without tights, you have leotards riding up, revealing too much sometimes, and generally being a distraction. It's a tough call, and I know there are some girls who throw a fit over the tights. But I think they need to learn what is appropriate clothing for a ballet class regardless. It's only for 45-60 minutes, so they'll survive.
As for the make-up, that's a weird one. You can expect the studio management to tell the girls to wear some make-up appropriate for their age for recital or other performances. But for dance class, definately not. In fact, I would say, for younger kids like your niece, make-up should NOT be permitted in class (tweens and teens, ok, as that is the norm now). And it goes without saying that gum chewing at any age is completely inappropriate in any dance class. (But I digress!)
If you are in an area where there are other options for dance studios, I would advise checking them out. Go observe some classes elsewhere. Talk to parents from other studios. Ask what the other studios'policies are. Bottom line is if what a dance studio is having your student do....or not do...doesn't seem right to you, go with your gut and seek out other options.
I would like to think that all studios are run with only the best intentions of teaching dance and helping kids grow in the activity. But there are, indeed, some studios that maintain questionable policies and practices. Go with what feels right for you and your dancer.
Good luck!