How to repair this hefty wooden fence gate?
The hinge is damaged, it's bent. You should either bend it straight or get a new one. The hinge has three holes for screws your only using two of them. That's putting extra stress on the two that you are using which is probaly why they pulled out. Hard to tell from the picture how bad the wood is split. I would not try to add any wood, if anything perhaps replace the bottom horizontal piece if it's split badly. If it was my gate I would drill holes all the way through and use a nut and bolt as opposed to wood screws to re-fasten the hinge. You should be able to find decorative ones that match. Someone else may come along with a better answer.