That's indeed very odd that the tractor was delivered with the bent arm. That usually happens by not having the stabilizers adjust right or by pushing something in reverse, like a box blade or something. The 3 pt is really meant to lift and pull.
I see a couple things not quite right though.
- The obvious bent arm, which needs to be fixed to get things straight again
- The lower pin brackets on the tiller, should be facing forward and not up. It's hard to see but looks like its mounted on a square tube and can be easily fixed by just flipping 90 degrees.
- The Pats hooks, which makes hooking implements easier but pretty much constraints most axis of movement as it makes the ball end pretty much useless. One of the big reason why the Euro style hook is better as it still retains the ball joint, allowing to freedom of movement in all axis. This may very well be the cause of some of the binding you're getting, however, once everything else is fixed, it should work just fine.
Found a picture of another tiller, which I believe is similar to yours, with the brackets facing forward: