Adrienne (#2 
) :
Attorneys are required to have trust accounts to keep client money separate from personal funds. They typically draw money from the trust as it is earned and send bills for any expenses in excess of your retainer fee. The amount of the retainer should vary based on the work you need performed - i.e. if you're asking for labor intensive search, match and counseling work, that would require a bigger retainer than a straight forward finalization. KWIM?? Our retainer for finalization was $500, roughly a third of the total cost.
The attorney can't really give you an itemized list of fees either (unless he/she is charging a flat fee) b/c she has no idea how much time things will
actually take - every adoption is different. She might be able to give you an estimate, but it may vary widely from your actual cost.
Also, I'd not be too worried about having not met the attorney if you've got good references (from people you know or from folks on the boards, etc.) If you're really concerned you can always contact the state bar association to see if there have been/are any pending, resolved or unsubstantiated complaints made against the attorney.
OP:
I'd ask yourself how often you expect the attorney to be in contact with you - .2 hours here and there will add up quickly if he/she bills by the hour. Also how far is his/her office from the courthouse or hospital (driving time costs money too!!)?
Some attorneys will charge you for everything (every email, every voicemail listened to, phone call made, etc., some will give you a freebie here and there. I'd ask about her overall billing philosophy. Is the attorney under any obligation to meet billable hour requirements (more of an issue at big firms).