One is whether consideration was present. For the second, there is consideration. The Restatement and virtually all jurisdictions hold that a promise for a performance amounts to consideration. There is a writing in this case - the letter containing O's offer. It appears to contain all the necessary terms - description of the subject matter, price, date, etc.
Most people sign the letters they send, so it seems likely O did.
It is only an offer. This writing does not necessarily show that the parties reached agreement or made a contract. This issue was discussed in part above, dealing with an option contract. But here J could attempt to rely upon the widely accepted rule in Restatement sec. 90 and cases like Hoffman v. Red Owl .