Yes you can. I have run the APU when I lost my fan belt. I was told it could be hard on the water pump on the APU unit as it is not designed for...
The hardest part of backing up to a loading dock is having to put up with an "audience". You all know what I mean. If there is nobody around you...
Even one weak battery out of a set of four can cause you grief with the electrical / charging system in the truck.
When they did your service, it sounds like they should have put in four new batteries, not just two.
I don't think the job requires to much effort. Initially hooking up hoses to tanks can be a pain in the butt, but you'll probably get the hang of...
Sounds like an interesting job. I've been hauling fluid for the better part of 23 years now. I always liked hauling fuel, especially from the bulk...