You are in a restaurant when you notice that your infant has suddenly become very still and her skin is turning an odd bluish color. what should you do first?

Symptoms you are describing are symptoms when a person is choking. airways are blocked and that's why she can't breathe, first of all, you should try and clear her airways so she can breathe without a problem. Firstly you need to perform a CPR on a choking person, so you can open up blocked airways. there are some So in Conclusion, your first step should be to open up the blocked airways. 

Making sure the equipment is cleaned daily and insuring proper hygiene is kept up with the working staff.

Yes, this is very true. specifically causing damage in the  dentrite.