The machinery in the bathroom is the pump for the potable water stored in the tank adjacent to the bathroom. The tank's empty, so the pump is running dry, hence auto shutdown.
I'll throw a bone. The lever is indeed one area that needs oil (and it isn't the top, obviously). Take a good hard look inside the generator's gearbox. Note the mechanical operation, what would rust and prevent the lever from being pulled and releasing the main shaft?
Honestly, we'd hate like hell to post up a screenie and give away the puzzle. Someone's gotta figure it all out (if they haven't already given up on it).
*Gun reload: Shoulder the spaz, reach down and in to pick up the shell pack (from the locker(s)), enigma. That's it, Bub.

**Getting aboard and off the Icabod is easy if you move the crate up against the hull. Hop down the same way, you shouldn't get hurt. Originally, all you had was the loose board near the docks to work with. That was a bit more difficult -
*** Tower Ladder: That's basically a physical puzzle, once you get the jump down, over to the area of the backside ladder, climbing the ladder is relatively safe if you ease on up there. I only hop myself up at the last rung. I personally use a side step down the terrain to get off of it to avoid nasty tumbles.