Ask HN: Client wants a refund. Am I legally at risk?

A client project of mine went very very badly. The requirements were not originally communicated, I was forced to drop the project due to time constraints. I handed over all code written in that time. The client is currently using my code, but wants all of his down payment back (50% of estimation). I believe he is not entitled to a refund, as he is utilizing my code. He is now threatening me legally, accusing me of fraud — charging him for services that were not delivered.

Am I actually at risk? Keep in mind, there was no contract in place.

I've posted his threats and my responses: https://gist.github.com/9de4e3450bdacf52b03d

Any advice would be deeply appreciated.