Yes, a transom eye is like a bow eye, but you get 2 of them and they are on the other end.
Transducers are ideally mounted half way between the keel and the chine to minimize turbulence. Yes they need to be below the bottom of the boat, maybe only slightly, with the trailing end a degree or so downward. The specific parameters are listed in the installation manual, and different types require different positions. I have had units that were mounted flush with the bottom (shallow V or flat bottom) and others an inch below. They need to align with the bottom of the river (or waterline, not the bottom of the boat.
Put it where it won't interfere with a trailer bunk. With that much rake on the transom you'd have to have awful long toes to hit it when climbing on the ladder.