Breakers are installed to keep the wires connected to them from overheating or to disconnect them if they short. If you are not sure where to put a fuse, imagine jamming any bare wire into the frame (ground). If the wire has a fuse between that short and the power source, the fuse/breaker will disconnect the power before the source overloads or the wire catches on fire--or both. If the short is between the source and the fuse, it will do you no good.
Breakers are resettable and also act like a switch, which is not always necessary. Fuses can be much cheaper, if you plan to use them, see if one or two styles will fit all your needs to keep things simple.
Blue Sea has some really clear charts for DC wiring here
They have a more in-depth set of charts as well on their web site (and an app too).
Looking at the photo, the size of the power source (alternator/charger/LiFePo battery) or the size of the draw (DC panel or inverter) will determine the wire needed (accounting for the length of the run) and the breaker or fuse required to protect it. So the alternator (starter battery) or the solar goes to the charger-both should have fuses. the charger goes to the LiFePo battery, needs a fuse. From the LiFePo you want to power an inverter and a DC panel to supply (& protect) a fridge, heater and other small loads. Inverter needs a fuse and so will the DC panel, the photo shows them sharing one. Start by figuring out how much power in amps (watts/volts) is going to go through each connection.
Size the alternator wires by using the max output of the alternator, fuse them for that or a little higher (again, see the Blue Sea charts)
Run your ground in the same size wire and count both wires as the total length for fusing.
With a DC-DC charger, use the max output of the charger to do the same calculation (the wires will be smaller), or just use #4 everywhere, as suggested.
Looking at the chart, notice how the shorter the run, the more current any given wire size can carry.
Your batteries will have a max-charge rate that will be a fraction of the total capacity and will last longest keeping to that threshold-- consider that when sourcing your charger.
If your inverter is 1000w x 1.25 /12v is roughly 100 amps, so from the chart above you can use #4 or #2 wire to keep the voltage drop minimal (3% or less)
The more the voltage drops, the greater the amperage you will need to get your peak wattage (amps x volts = watts).
The shorter your wires, the less resistance you will have and the less voltage drop you will see.
You can measure voltage drop with a volt meter testing the source and then the end of the run- the difference is the drop.
The "70 amp breakers" in the photo are for what?
On the left, it protects the solar battery output from overloading the wires supplying the inverter and the DC panel. if these wired are not the same size, use separate fuses.
The panel is probably rated for 100A and so is the inverter, but if you use them at the same time (at max power, pretty unusual) they would trip a 100A breaker.
You may want a bigger wire if the breaker is for combined output. Regardless put this breaker as close to the battery as possible--any wire between the two is basically unprotected.
On the right, you are protecting the wire from the solar controller/DC-charger input, so the wire+fuse are per the charger output as mentioned above (looks like 400w or about 33a max).
Again, put the fuse next to the charger. Generally, any wire less than 12" need not be fused, but it is important to protect it from damage.
A simple way to make short connections is use a 1/4" x3/4" copper bar drilled to fit the 2 posts of the charger & breaker. wrap any exposed area in heat-shrink or electrical tape.
The cross section of the bar is about the same as 4/0 wire, 1/8" bar would be a little beefier than 0 gauge wire- all well beyond what the situation calls for.
Personally, I would wire the line from the charger into the output side of the larger breaker protecting the inverter, not the input side as pictured. The charger is adding power to the battery, so it will not change the max output calculation you use to size the output/inverter (left) breaker. If that is at the positive battery post, any direct short in the wires beyond it will trip the breaker, so the line from the charger has a measure of protection from it too, even if it will never carry more than 40 amps into the battery in regular operation. Having a breaker at the battery will let you isolate it if you need, which can be helpful for repairs or troubleshooting.
Your busbar is probably a chunk of tinned copper tapped for screws. It will only be insufficient if the cross section is smaller than a wire you would need to run 125% of your max current through, and even then it will likely be fine.
As you can see above, you don't need much bar to carry a huge amount of current. The suggested 250A rated one is more than fine.
Use one that has enough screws for your system, attaches easily and has a cover if you want one.
With all these separate components, it may be worth using a single fuse block to make all of your connections and just use breakers at the two battery posts.
A Blue Sea 7748 block has 4 high-Amp spaces (30-200 amps) and 6 smaller fuses (1-30 amps) as well as a negative busbar. The 200 amp total rating will likely cover all of your needs.
Run a short wire from your DC-Charger to a 40A fuse slot.
Run as long a wire as you need to the inverter and fuse it at 100-125A.
Your heater, USB plugs and fridge (and possibly lights) will run off the small-fuse side.
The positive lug is connected to your LiFePo battery (with a breaker at the post).
All the negatives will run to the busbar--from the inverter, charger, LiFePo, heater, etc. and you should also run a cable back to the starter battery.
You should also fuse the solar at the panel with a waterproof block to protect those wires and allow you to disable it when you need-- like when you take it into a shop and don't want to electrocute the mechanic.
With this sort of arrangement, most of your connections are in the same place, which is fairly compact. The second battery and the inverter can fit wherever you have room.
Lastly consider getting DC chargers for the phone and computer gear rather than converting to AC with the inverter and back to DC to charge.
The inverter is most efficient running near its rated capacity, much lower draws will be far less efficient. Installing a few 10A cigarette style outlets will let you use standard car chargers for your electronics, or you can get dedicated USB outlets to do the same thing.
Hope that helps, & remember, if you screw-up you can burn your Jeep to the ground!
