Wrench light and check engine light after new battery?

My husband originally replaced my water pump. After getting everything back together, the next day the battery was completely dead. Changed the battery wrench light and check engine light came on. Next day car wouldn't start without a jump. When trying to turn my car off, the engine kept running even though it had been shut off. It ran for a minute, shuttered, then shut off. We did a BMS and replaced some relays since the code reader said they were bad. Still have a wrench light and check engine with the engine not wanting to shut off immediately after I push the button to turn it off.