What exactly is The Royal Ballet?
It is a ballet company at the Royal Opera House. It is located in London, England.
Do they teach ballet or is it merely the site where ballets are performed?  Or is it a combination of the two?
They have a school specifically for teaching them called the Royal Ballet School.
That is very cool.  I assume that they are very well-known?  Personally, I know nothing about ballet.
I think they are pretty well-known. They house about 100 dancers.
Do you know the statistics of the dancers?  All men, all women?  50% of each; etc.?
No I do not unfortunately. The Prima ballerina is Dame Margot Fonteyn though.
What interesting facts make her the prima ballerina?
It is who is considered the most notable of all the female dancers.