There should be no fear of shutting the generator down with the bucket in the air. With the bucket raised there is no load on the pump. Also just for your information all cylinders on an aerial lift are required to have holding valves built into the cylinder, in order to hold a load. So to check the level in your gearbox I would raise the boom ask the way up in the air, you can kill the engine if you want, then I believe the level plug is located on innermost side. I'd only remove the cover if it's low, since I'd be worried about breaking those bolts off. Now if you had to remove the gearbox you would have to be more creative, as you would have to secure the boom from rotating, however I don't think it will come to that. Torque specs for the cover bolts would just be standard dry torque for those fasteners, I can't remember if they are 1/4 or 5/16 but you can easily look up the torque, but it's not critical.
Back to your generator, a lot of those units had the ability to start and stop the generator from the basket, to save fuel and reduce noise. Feel free to continue to ask questions, I'm happy to help and keep you safe.
