Hi,
a/ I know a small board hung in front of a shop is called a shop sign or signboard Please help me find the suitable words to express a small board usually hung in front of a doctor's or a lawyer's . You could say a sign. In N. America, some doctors and lawyers refer to this as their 'shingle'.
b/ What's the meaning of " attorney at law " ? Is it the same as " lawyer " ? In layman's terms, yes. But the terms used for different kinds of lawyers can vary a lot from one country to another.
Best wishes, Clive