The contract looks relatively standard and I understand most of it. Plus we have already signed (but closing is not until mid August). Even so, is it normal to have a real estate lawyer read it over and advise us before closing?
Yes, I would advise you retain a lawyer. You will need assistance with the Closing Statement. Also, you will need title insurance (every states is different), but usually you can the legal advice if you give the title/closing to your lawyer who will assist you with all aspects of the closing.