Welcome to the forum - we were all new to the TM at some point, so don't be afraid to ask questions...we're a helpful bunch
I'll take a stab...I'm sure others will also jump in: (edit - Scott already did while I was typing...
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1) When you're connected to 'city water', the pipes fill up with water, however there is likely air in the hot water heater tank, so it can't fill with water until you open one of the hot water faucets so the air has a place to escape. After hooking up, but before turning on the hot water heater, we'll normally run the hot water faucet until water flows smoothly without the burps and gasps you get when there is still air in the system.
2) When using the fresh water tank, the pump needs to be on for water to flow thru the sustem (including to the hot water heater). Same idea as #1, but just turn the pump on instead of connecting to city water supply. Once the system stops burping, it's ok to turn on hot water heater without fear of burning the element.
3) Yes, there is an overflow built into the inlet. If filling to fast and not allowing enough room around the fill hose for the air to leave the tank, it may burp water out because the tank still has air. So, I'll usually pull the fill hose out for a moment, then stick it back in to make sure air isn't forcing the water out rather than the tank being full of water.
4) I don't do it when filling - I'll wait until when I arrive and am setup at the CG, just before turning the hot water heater on.
5) No - grey water and fresh water are seperate.
6) You need to turn off the hot water heater while in storage. Using the electric side of the TM it is easy to forget. For me, I prefer to always use propane for the hot water heater, that way I don't forget to turn it off when stored.
7) There are low point drains (newer models have 4) that I believe should drain the entire plumbing system (living in SoCal and camping throughout the year, I have not used them, as I do not have to worry about freeze either). The drains are just small plastic valves connected to flexible tubing. On my TM there are two on the front street side of the TM and two towards the back.
8) You should be able to get an assortment from an auto-parts store. The fuse panel is behind the plastic access door on the lower bathroom wall. You can record the different fuse amperages and make sure the kit you get includes all that you need. There is also a fuse near the batteries...TM ships with a glass fuse in a plastic housing that is prone to overheat and fail. Many of us have replaced with a blade fuse.
9) see #8
Hope this helps!
--jim