Yes and no. Yes, there could be a verbal contract but there would have to be a clear understanding hich s best documented in writing. No, an attorey cannot represent someone without authorization. We would need more facts to specifically address your questions.
I am licensed in California only and my answers on Avvo assume California law. The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case. No attorney-client relationship shall be created through the use reading of this response on Avvo. You should never delay seeking legal advice, disregard legal advice, or commence or discontinue any legal action because of information in this response.
In California, a lawyer can represent a client without a signed retainer agreement if: (a) attorney's fees will not exceed $1,000; (b) attorney's fees are non-contingent; (c) the client states in writing that he/she does not want a written fee agreement; (d) a writing is impractical for other reasons; (e) the client is a corporation; (f) the lawyer acted in an emergency to protect the client’s rights; OR (g) the representation is for routine services for a regular client. But, generally speaking (so, there are exceptions) a lawyer must be authorized by the client to represent him/her. (You really do not provide enough facts for any further analysis.)