A contract has to have the essential elements required to be binding, it doesn't matter what the medium is.
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In general, as a matter of law, in order to be binding and enforceable upon the parties to an agreement (or contract) the agreement requires: (1) an Offer; (2) with Acceptance; and, (3) sufficient Consideration. In addition, there must be a meeting of the minds to the elements of the agreement between all the parties, which is made without fraud, duress or undue influence. Furthermore, for the agreement to be binding and enforceable, the parties to the agreement must not be under any legal disability or incapacity when the agreement is made. Finally, binding and enforceable agreements or contracts can be made either orally or in writing.
The State in which your agreement or contract was made (or, possibly, the state in which your agreement or contract will be performed) has its own unique statutes and Rules which governs both Contract and Evidence Law. Since that information is not provided in your question, I will presume that NM is the State where the agreement was made and will be performed. Therefore, NM provides its own unique statutes and specific Rules for the content and timing required for an agreement or contract to be valid and enforceable in NM.
The specific answers to your questions, which will be determined by the NM statutes and Rules which govern Contract and Evidence Law, can only be obtained via your personal consultation with an attorney licensed to practice in NM who knows the applicable NM statutes and Rules which are above described for you. You should be prepared to take with you to that consultation all of the texts related to the "deal" here at issue.
You should also be prepared to pay a fee for the NM attorney's consultation, review and advice. The amount of that fee (if any), and the terms for the payment of same, should be agreed upon between you and your attorney before starting the consultation.
The response given here is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change. Attorney is licensed to practice law only in the State of Ohio. Responses are based solely on Ohio law unless stated otherwise.