Would a fox be able to lift the wood without the hinge lock? Say if it was just tied directly without the hinge to block lifting it.

If not a fox, a raccoon can.

Here's my fun everything likes to eat chickens story. When we first built our house, nobody had ever lived within about 2 miles of our farm. There were coyotes everywhere. So I spent a couple years trapping and shooting them after they ate a couple of my chickens. Then came the racoons. They ate some chickens so back to trapping and shooting. Then weasels and minks. Except they could get into the coop through the windows in the wall that were covered in wire and 6' off the ground. So, more traps. Now it's bobcats. Oh, and don't forget the stupid red-tailed hawks and BALD FUCKING EAGLES as well. No trapping or shooting those bastards.

Everything. Everything eats chickens. I'm surprised I haven't seen a damn frog eating one of them.

I'm not around a lot of foxes, but I imagine so: They both burrow and hunt burrowing prey, so "lift and scrape this obstacle of the way" is in their skillet.

Probably. I used to have a pet parrot that learned how to open its cage from watching me unlatch it every day.

Probably, but it'd be pretty trivial to add some weight to the door.