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C is corrent. A payment of less than the originally agreed-upon price will serve as complete discharge of an obligation under a contract only if there is a bona fide dispute as to the amount owed, and both parties agree to the lesser sum. In this case Milo and Nord had agreed upon a fee for services of $45,000; thus, this debt was liquidated since the amount was certain. And since Milo had completed the work to Nord’s satisfaction, no bona fide dispute as to the amount owed arose; thus the debt remains liquidated, and Nord will be required to pay the full $45,000. The fact that Milo had endorsed and deposited the check which Nord had conspicuously marked as constituting payment in full is of no effect since the obligation was a liquidated debt, instead of an unliquidated debt.
A is incorrect. This contract is not covered by the Statute of Frauds because the terms of the contract are less than one year. 
B is incorrect.  The other bids are not relevant.  Milo and Nord made an agreement for $45,000.  If Nord did not like Milo’s price, Nord could have hired one of the competitors, but Nord did not do so.  Nord is bound to the terms of the original bargain.
D is incorrect. An accord and satisfaction involves an agreement for a substituted performance rather than the original obligation in the contract.  For example, Nord could have asked Milo if Milo would take $30,000 and Nord’s valuable stamp collection rather than the $45,000.  If Milo agrees, then there is an accord.  Here Milo never agreed a substituted performance.  First this is a lesser performance, not a different performance; second since the debt of $45,000 is undisputed, Milo’s cashing of the $30,000 check is not an implied agreement to take the lesser amount.