HELP: Probate Court etc.?

I'm going to try to make this as simple as possible. I need some advice (lots), my lawyer is making no effort to help me.

My great grandmother passed away in 2009, and I (and my brother) inherited her estate. My brother does not really bother to help with anything, so all this has been put on my shoulders. When my grandmother passed I had spoke with her lawyer, and he was supposed to be getting everything done, so I would be able to sell the house. I have been calling to check up and nothing has been done. Now, 1.5 years later I am being asked to pay $350 for probate court from the lawyer? I am young and have no idea what I am doing, but I need all this to be done right, and as quickly as possible, since the lawyer wasted all this time already. So now to get to the point, is it possible for me to take this to probate court myself? If so, how do I do this and what am I supposed to be filing? And approx how long does probate take?

Also, my great grandmother had a safe deposit box, I had given the lawyer the key to it (because he asked), and asked him to get everything out for me. There is family herilooms in there that mean very much to me. Now, once contacting him he tells me that he cannot open it because his name is not on it. The box only has my great grandmother's name and my father's name. But, my father has already passed (shortly before my great grandmother), so now what happens with the safe deposit box? Can I never retrieve anything from it?

Adding to the complications, I live on the other side of the US, and am going there in March for a weekend to take care of the things inside the home. I will be doing an estate sale with the belongings. Is there anything I should know about this? While I am down there I want to do as much as I can, so what else should/can I do?

I know this was complicated, but I really need help with this. I am feeling overwhelmed and need this all to be taken care of as soon as possible. Thank you in advance for your help.