I would intrepret this as being inappropriate and possibly a bad sign.  Once, in a laughing voice, is a joke, but twice...hmmmmm.  The client-provider relationship by necessity has to be emotionally "at arm's length," as you say, unless there is a mutual decision to carry it further.  This has nothing to do with the provider's attention or willingness to please you.  If you had been seeing her regularly for some time, there might be a basis for her to have developed a fondness for you, but the first session?  I think it rather unprofessional and downright tacky to even mention the existence of other clients.  What man, even if he is paying for it, wants to think he is one in a long line?  There are ways for her to deflect this to other, more facetious pillow talk, and if she isn't making you feel that you are the most important and ONLY man in the world during your time together, she is lacking an important grace.  Try another provider, dear heart.

Assuming that she knew of your limited experience, she may have been testing whether you were "stalker material", in case you were interested in repeat meetings.  There's always a possibility that she fell madly in love with you and hoped you'd want her to quit and run off with her.  She may also have a jealousy fantasy.

I've gotten into some discusions with ladies about other ladies I have seen.  Things like humorous happenings or strang behaviors.  Of course, no names mentioned because of the privacy issue.

That's a totally in appropriate question and I've never heard of any provider asking that before.  

Is it possible she's a very insecure person and wanted to think you were jealous to make her feel better about herself?