"How do I find a competent estate planning attorney in my specific area? How should they be billing for the settlement and administration of my mother's estate?"
You should make inquiries of bank trust officers (not general bankers but specifically those working in a trust division of a bank, trust company, or major financial firm). Accountants who have experience in estate work can often make informed recommendations. Unfortunately, the recommendations by most lay people may not give much assurance of obtaining the quality of assistance you wish since it might be difficult or impossible for most lay people to differentiate the technical capabilities, staffing, planning expertise, etc. of an attorney specializing in estate administration.
You are probably best off seeking someone or a firm that spends a substantial portion of their time with estate planning and, in particular, administration.
Billing is a critical question. In the vast majority of cases, there is no correlation between the size of an estate and a percentage billed for the work to be done. Your best bet is to handle work solely on an hourly basis and pay on the basis of detailed bills.
As a final note, be cautious of hiring somebody simply because you see their name heavily advertised in local papers, especially if these are advertisements for probate avoidance techniques.
Caution: Although significant portions of an estate administration can be routine in nature, many estates have one or several complex or potentially difficult issues. The issues may relate to legal matters, such as title to real estate, tax matters, estate administration issues, and often merely interpersonal matters to be handled delicately. It is always strongly advisable to hire an estate administration specialist, at least at minimum for an initial meeting to review the overall estate and the steps that need to be taken. Since estate administration varies so much from state to state, you really should consult with someone who is experienced in your locality.