What exactly are providers looking for when they screen potential clientele?...especially for first time users with "no references"? Is it hard to make a date with a well established provider with long record of good reviews?

probably ask for your work #, cel #, occupation, real name, and might ask for you to show I.D. upon arrival. Some providers may ask for more extensive info. If you see well reviewed providers, you need not worry about them divulging any of the info you gave them.

Or a mugger, rapist, murderer etc

Will they call your work #? I only wonder because I work at a company that has only one phone and everyone recieves personal calls via their cell phones.  There is no other way that a provider can verify identity via email for example or via email and photos?