Your Multiplus can pull 3,000 watts. Divide that by 12V and you get 250 Amps, just for the inverter. Add additional amps for your other DC current.
AWG-2 cable is far too small for what could be 300 Amps.
The Victron Multiplus that you're using specifies two paralell runs of 50mm cable. The AWG equivalent of 50mm is AWG-1, sometimes called 1/0 "one aught". AWG-1 is twice the thickness of AWG-2, and they're calling for a pair of them. And that doesn't even include any additional DC loads.
Reading the manuals are important, getting educated on wire-size is important.
You also haven't talked about what kind of fuses you have. That is critically important, as different fuse types have very different characteristics. Here is a good primer on fuse-types:
- note this video is produced by Explorist.life, which has an excellent series of building RV power systems.
Your questions:
- Fuse Sizing: What size fuse should I be using given the current setup and the components involved?
RTFM. Victron recomments a 400amp fuse JUST for their Multiplus.
4 400 ah batteries in parallel can put out a MASSIVE amount of energy in case of a short-circuit. You MUST use a T-Class fuse to protect downstream components.
- Battery Connections: Do I need to install a fuse on each battery before connecting them to the bus bar? Currently, all four batteries are connected to a single 400-amp fuse at the Lynx Power In.
Fuses should be placed as close as possible to the battery, not the bus-bar. You can put a Marine Rated Battery Fuse on each battery. (MRBF).
What this video on where to put fuses. :
- Cable Upgrade: Should I upgrade to 2/0 gauge cable to handle the load more efficiently, despite the high cost of copper?
YES! If you can't afford the copper, you can't afford the RV. You can do a pair of 2/0 cables, or a single 4/0 cable.