Here's what I can see from the pictures. Please correct me if my assumptions are wrong.
picture 1) Like the poster above, the green light means the charger is "on". Depending upon what the green light is doing, it is in a different charge mode.
http://www.progressivedyn.com/charge_wizard_9105.htmlpicture 2) The running lights are 100% independent of the charger and house lights. The docking lights look like they are controlled by relays from either the reverse lights on the truck or the switch on the camper. Either way the power comes through that missing dock light fuse. Are the dock lights actually working, even with shore power connected? The vibration you feel is probably a breaker or relay that is cycling rapidly (i.e. not working).
EDIT: The vibration is almost surely the relay closest to the breaker. With shore power disconnected, you're probably getting a really low voltage to the relay coil and it's not able to fully engage. Once you provide shore power there is enough to pull the relay all the way closed. In either case your docks lights shouldn't work without the 20A fuse in slot #2.
The 2-pin device with all of the large black wires is a self-resetting breaker. The single black wire comes from the battery disconnect (master) switch. The other large wires on the right side go to your load center (for all of the interior lights, radio, etc), fridge, converter, jack controller and probably solar and/or generator starter. I'm guessing the smaller black wire from the missing dock light fuse (#2) is also connected where those large ones are.
The 2 black cubes with the red, green, white, black and blue wires are the relays for the dock lights. Are they what is vibrating or the breaker with the big wires? Either one would make the fuse panel seem to rattle since they're all bolted down to the same plywood. If you want to eliminate the dock lights as the cause, you can pull those pin headers off the relays temporarily.
pictures 3-4) The spare fuse in the toilet paper compartment looks like an add-on. The smaller wire comes from the what seems to be the 12V battery wire. Does the other end go somewhere like a battery warming blanket or ??? Follow the wire if you need to know but either way I don't think that fuse is the issue.
The easiest way to narrow this down is to leave the shore power disconnected and then start tracing the +12V from the battery with your meter. It looks to me (assuming from what I see in the pictures), that it comes from the battery box, through a breaker, then the cut-off switch then up to the main breaker which spreads out to the various loads. Check for 12V at each of these places with ground connected to the battery (or a wire inside known to connect to the battery -). The ground should be a white wire the same size as all of the large black ones. I see them connected to the ground bar at the bottom of picture #2.
Let me also ask one dumb question: Do you have the battery polarity correct? White is ground (neg) and black is 12V (pos).
Starting at page 94
here there are wiring diagrams showing a lot of detail.
EDIT: Based upon the vibrating relay, my guess is you will find very low voltage on the clump of black wires with shore power disconnected, especially if you turn on the dock light switch. If it's also low on the single black wire, the battery disconnect switch is suspect. You can jumper across the back of it for testing purposes. If the single wire is at 12V, the breaker is bad and needs replaced. You should also cycle the battery disconnect switch a few times to be sure it's seated well.