Use at least #2 for the inverter. 2x#4 is the same as #2. I find lugs and connectors to be problematic and suggest you reduce connections wherever possible. I.e. #2 (or 00) rather than multiple wires. (I used #4 between the batteries. Ok, but a tad light)
20a charge controller should be fine for 400w of solar. #10 wire should be fine for most circuits. #14 should be fine for your actual 12v loads.
The alternator should really be a proper charge controller and, depending on the run should be #4 wire as a depleted battery will draw a lot of current.
I think the separate shore circuit is a great idea. I wish I had done that.
I would put in disconnects between the battery and everything else and on each external power source (alternator/solar) and the load center. This is for convenience as well as protection. Appropriate sized resettable thermal breakers are convenient. Use a quality brand. I use mechanical products.
Consider a combo a solar/alternator charge controller. I have had good results with the Renogy unit and I see other reputable brands have competing product (kisae). Less wiring (see above) and better battery management.
20a charge controller should be fine for 400w of solar. #10 wire should be fine for most circuits. #14 should be fine for your actual 12v loads.
The alternator should really be a proper charge controller and, depending on the run should be #4 wire as a depleted battery will draw a lot of current.
I think the separate shore circuit is a great idea. I wish I had done that.
I would put in disconnects between the battery and everything else and on each external power source (alternator/solar) and the load center. This is for convenience as well as protection. Appropriate sized resettable thermal breakers are convenient. Use a quality brand. I use mechanical products.
Consider a combo a solar/alternator charge controller. I have had good results with the Renogy unit and I see other reputable brands have competing product (kisae). Less wiring (see above) and better battery management.