the Flow Control Valve you've got there is great for tilling, and pretty uncommon! Helps keep the tiller from pushing the tractor. You set the lever on the dash to full forward and then dial in speed using the flow control valve's lever there.
It sounds like your 3pt hitch and mid-lift cylinder (the deck cylinder) are plumbed opposite of each other. This isn't how Case instructed it to be installed, but it's a good solution that allows you to use the deck with the tiller connected or use the tiller with the deck connected. In the OEM configuration (just the two hoses swapped underneath the tractor from how you have it now) when the deck is all the way down the tiller would be dragging on the ground, so you'd have to drop the tiller to mow. Or you'd be trying to till your garden but you're dragging the deck through the dirt at the same time.
I've never heard of someone tying the 3pt hitch into the rear axle though, that's a new one. The heims on the tie rods are common "upgrades".