I realize I'm coming in late to this string but wanted to add my thoughts.
First thought and only because it's your last post. Can you go to the local dump and grab a battery out of the recycle bin to save on the core charge?
Yes definitely add a fuse or circuit breaker to every wire that comes off the positive side of the battery. The fuse is to protect the wiring and trailer from burning up.
I know you want to add the inverter to power things. Inverters are cheap and work well. But you should also consider adding a USB outlet near your bed for charging the phone overnight. It sounds like you are familiar with crimp connectors so I would go this route. You will need an interior cabinet or maybe the base of the bed to mount to and drill one maybe two holes to do this.
This plug uses crimp connectors. You can wire positive and negative straight to the batteries. You can also do as I did and wire to an existing 12v wire like the overhead lights. the plug I linked is about $5 more than other plugs. But that is because it was the only one I could find that was non illuminated as in no LED constantly drawing power.
Plug on Amazon 
You will probably also need a 1" hole saw.
Hole saw on AmazonRun some 16 gauge wire and if going to the battery put in a 10A fuse.
10 pack fuse holdersAll in all under $30 to be able to plug your phone in next to your bed at night with no inverter.