Momentum is what matters. KE is just what they publish. KE corresponds to a bow efficiency, since the potential energy you draw into the bow is what gets conserved as you release the bow. That's a different conversation entirely, but arrow KE vs. draw power curve speaks to bow efficiency.

Momentum is what penetrates. A .30-06 and a .45-70 can have roughly the same energy, but the momentum is considerably higher for the .45-70, which is why it earns a reputation as a heavier hitter. Similarly, heavier arrows, even with the same KE as a lighter arrow, will hit harder and penetrate better.

You have this backwards. Mechanical broadheads need a minimum degree of KE or momentum to deploy. A heavier arrow will deploy a mechanical broadhead better (read: more reliably) than a lighter arrow, and provide better penetration thereafter.

The opening action of a mech robs some momentum and KE from your arrow. When you're shooting a 40ft.lbs. bow, that stolen power might be significant enough to be detrimental to your arrows killing power. Where KE is the same, the added momentum of the heavier arrow will drive it open and penetrate better.

Limited KE broadheads often have smaller blades, so essentially the stolen deployment power is the same, but the arrow is able to penetrate better due to less blade drag in the wound channel. Overall, this is a negative effect as compared to a fixed blade broadhead, since that means less damage along the wound tract, but a small blade that exits is better than a big blade that doesn't in terms of tracking and blood loss (killing speed), so it's a bit of a compromise.

82-86ft.lbs. and 269fps is more than enough to deploy any mech on the market. In fact, you might find that it's even over powered for many mech models, so you may actually break certain broadheads even without hitting bone.

That's not to say that we should all be shooting 700grn arrows just to kill deer. I've killed plenty of deer with ~300grn arrows around 250fps (I can't recall what my recurve puts out, but I'm pretty confident that it's less than that!). They're no more dead these days when I put 450grn arrows through them at 330fps. But I CAN kill them a lot further out there than I used to be able, with a higher rate of recovery.

I've set up some 750-1100grn arrows, tried them on deer, but ultimately, it's a mess. Way too slow with way too much drop to be practical, and my hunting pack got really heavy hauling around a handy-man jack to pull them out of the ground after they exited the deer...