Yes you do, there's a bit of weight in those doors. My tudor has a 4" chop, there's plenty of room for the cut.
I have all 3 and about 6" off the top. I have seen a lot of cars built with two hinges, both ways, with the top hinge gone or the middle hinge gone, it would work either way.
i have 7.5 inches out of my sedan and the top hinge is gone and works just fine, but i would say if you can keep it then keep it
Definitely keep the top hinge. Door drop can be an issue even with the hinge but it is even worse without.