There is a provider I have researched and want to see.  I have called her several times over the past week and every time her phone is turned off, I get her greeting, then the system says "Sorry that mailbox is full".  How normal is this?  Seems kind of unprofessional, but she probably gets a lot of calls.  Maybe she was not working over the holidays. Her website does not list any email address for her and specifically says "No texts!".  I think I will try for a few more days, then move on.  Any thoughts or advice?

either she is not interested in seeing you or just rude.  Find someone else.

perfectly normal..have patience..the little head always gets anxious..

I reply to emails right away and obviously if I had a phone line for this I would also like to clear up my messages ASAP.
Sounds unprofessional but not unheard of, if you are really really interested on seeing her wait a couple of days and try to call back. If you get the same message then it is time to move on to someone with better business practices.

If she doesn't then that might tell you something ... If she only takes calls and texts professionalism isn't her forte. I have on several occasions had a full voicemail box but voicecalls are not my preferred form of initial contact. When you use a throw away cell often you only get a small number of messages before the box is full ... Given a holiday, a day or two off or just a busy day, my box can be full in a days time (no pun intended lol).

I don't care for it at all because frankly it closes off gals I would like to see...  some gals work on the 'first to arrive' business model.  
When they need money, they throw up an ad.
They turn their phone on & give anyone who responds the call point.  The first to arrive gets accepted.  
She shuts off her phone until she's free again.  Other guys who are circling may or probably are not still be there when she's free again.  She never listens to any VM or calls any back...  why waste minutes listening to guys say 'Where are you?'
As soon as the guy is out the door or maybe before...  she turn her phone on & the next to arrive...    
There is the natural tendency to rush because the more she sees the more she makes.