A will and trust lawyer Is doing my probate I am not happy with the outcome I’m not happy with the billing and I’m not happy with the way the case is

I can't tell you whether this person is a "real probate lawyer." Any licensed attorney may legally handle a probate. An attorney who focuses on wills and trusts will generally have experience with probate.  $11,000 sounds like a large deposit. Typical deposits are just to cover costs, which are around $1,500-$2,000. The attorney collects the fee for his or her work at the end of probate. The only situation where a large deposit, to cover the entire probate fee, could be appropriate is if there's a house in the probate and you intend to keep the house. In that case, many attorneys request the entire fee up front, to be held in their trust account until the probate is completed. Otherwise, they risk not being paid. If he has filed for probate, gotten a hearing date, and sent out the appropriate notices, he's probably doing his job. If not, you may need to get your money back and switch attorneys. 

You can hire another lawyer to substitute in.  Most will and trust lawyers do handle probate.  You can check with  the local probate court to see whether the fee meets the court's standards.