Don't know what happened to Q22, it's the first time I ever saw one smoked like that. I had a bad feeling when I saw all the burn marks around it, when I picked it up, I just had to desolder the inside pad that provides heatsinking, the whole outside set of PCB traces were toasted and gone! A reversed battery could explain it I suppose, you can get a lot of current from those. I wrote that board off as a loss.
Which of the '244 chips is the one that is connected to that FET for the relay control? It'll be a bummer if the processors are gone.