Yes it is normal.....let her know that private parts are private parts and there is a time and place for everything. In front of mommy and other people with other people is not apropriate!
Spending the night at other peoples house is over rated...play dates are better in the day and age...with all that kids can get into, is it the safest? Times are different!
I have boys that play with themselves all the time.I remind them daily what is private and appropriate!
As parents we have to remind them of what is acceptable, like table manners and what to wear and how to use their bodies.
The world today is very open and exposed re sexuality.
It is harder to raise kids today than ever before!
Take one day at a time and know that they are children and the most important thing that you can do is keep the communication open.
you are not alone!