Final answer:
Joe Contractor has rights under the terms of the original proposal, but the amendment made by the Owners raises questions about contract formation. Impossibility of performance may excuse Joe's failure to meet the deadline, but he must prove it was unforeseeable. Also, Owen's refusal to pay could constitute a breach of contract if valid terms were established.
Step-by-step explanation:
Joe Contractor's legal rights and potential liabilities depend on the contract that was amended and not countersigned. The original proposal by Joe became an open offer once the Owners altered the terms and made a counter-offer. Without Joe's acceptance of the modified terms, specifically the ten percent surcharge on materials, no binding contract with these new terms may exist.
However, Joe began work, which could imply acceptance of the terms by performance, but this could be contested. Concerning the completion date, Joe's excusable delay due to his assistant's illness could be argued under the doctrine of impossibility of performance, although this often requires the impossibility to be unforeseeable, and the burden to prove this lies with Joe.
The pricing discrepancy for the ivory faucet handles suggests a possible mistake on Joe's part, which could permit him to adjust the price if he can demonstrate that a mistake was made and that the Owners knew, or should have known, about the mistake. In absence of an agreement on price, Joe may only be entitled to the reasonable value of his services, which could be influenced by the market rate Owen mentioned. Owen's firing of Joe and refusal to pay the agreed amounts could be a breach of contract if a contract was in fact formed and Joe was willing to cure any defaults.