If we back out of a loan can they keep some of our down payment?

We been through so much stress in getting a home loan for this house we fell in love with. Our offer was almost $ 10,000 below asking price. We just had our inspection close to our closing date. Our closing date has been extended but from our inspection we found out that the heater and a/c does not work. The bank does not want to fix anything they did not touch when doing repairs. The house is still a high price to us. The price wouldn’t have mattered but now we have to put more money into the house for repairs such as the a/c, heater, changing all outlets and sprinklers. We did come across another home that is bigger in house size and a bigger lot for a cheaper price. We are just so lost in what to do we been through so much in trying to get this house and now we come across a bigger house at a real good price and wouldn’t mind if we had to make repairs like the other house. We just want to know if they can keep any of our down payment if we back out. We live in CA and the mortgage loan is in New Jersey if that matters. By the way both are foreclosures.
It is a FHA loan. So does that mean the appraiser didn’t do their job since the heater doesn’t work?

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