Your diagram is a little confusing to me because it mixes 120V and 12V circuits without a lot of indication of which is which. Also, 120V AC circuits don't have a positive and a negative leg; there's a hot and a neutral (and a protective ground), but the polarity of them with respect to each other alternates. However, I think I'm able to suss out what you're trying to do.
You have one rather important problem on the 120V side: the charger/converter circuit is not connected to a branch circuit from your electrical panel. That's almost certainly not acceptable per the NEC. However, connecting it to the panel after the transfer switch does lead to some potential difficulties to solve: you don't want the charger to be on when running off of inverter power, as you'll just waste battery power trying to recharge the battery from itself (with the power waste coming from the inherent inefficiencies in the inverter and the charger).
The ideal solution there is to have only selected circuits switched between the inverter and shore power with the transfer switch. There may also be other things you don't want off the inverter power--commonly in a camper these might include an absorption fridge, an electric water heater element, an air conditioner, or (with a 300W inverter, at least) a microwave. If you partition your electrical circuits appropriately you can make it inherently impossible to run them from inverter power.
A simpler and cheaper solution for small setups like this is to just have some outlets dedicated to inverter usage. This eliminates the need for a transfer switch entirely. If you're plugged into shore power, you can continue to use the inverter outlets off the inverter indefinitely since the charger will carry the load. (A larger inverter might require a bit more care and consideration in that regard...with a 300W inverter and a 45A charger, you'll still be charging the batteries a little even with the inverter running full bore.)
The battery isolator is quite possibly unnecessary in your situation, assuming you're using a 7 pin trailer connector to get the charge current. If the trailer connector power is switched on the truck (some are and some aren't), you won't be able to deplete the truck battery by using power in the trailer. Most trailers do not have an isolator setup.
The surge protector you show is of rather limited value. It's basically the same as a surge protector power strip with a GFCI added on. It does not provide any protection against sagging or moderately high voltages like an EMS unit does, nor against wiring errors in the outlet you plug into.
In terms of wire sizes, etc: for the AC side, this is pretty simple as it's defined by the NEC. For 30A circuits, you use 10 gauge wire (or heavier); for 20A, 12 gauge wire (or heavier); and for 15A or less, 14 gauge wire (or heavier). Given the length of the wire runs you have in a trailer, heavier wires are a waste of money. The current rating of the circuit is basically determined by whatever circuit breaker is upstream protecting it.
For DC circuits, there are two considerations. The first is fire safety and heating, which basically means not exceeding the safe carrying capacity of the wire size. The second is voltage drop, which one wants to minimize as much as practical to avoid wasting power. The current carrying capacity of the wire does not vary with wire length, but the voltage drop does, so for longer wire runs you often want or need to use heavier wire than would be necessary for short runs.
The wiring should be protected (on the positive side, assuming a standard negative chassis ground) as close to the power source as practical with a fuse or circuit breaker of some sort that is not larger than the safe current carrying capacity of any wire it protects. In situations where there are more than one possible power sources, it's necessary to analyze the circuit somewhat to figure what the total current at any point could be and figure protection appropriately. What you want to ensure is that a short to ground at any point would not cause any wire to carry more current than it safely can.
The charger has output fuses built in. One common approach at the battery bank is to have a large fuse at or near the battery positive terminal for everything in the RV(in my motorhome, this is a 175A fuse). From there you have wires going to whatever large or special things need connection, with fuses or circuit breakers appropriate to the situation. For the inverter, the documentation probably gives a suggested size, maybe around 50A. For the connection to the charger, 50A would also be appropriate. For connection to other 12V circuits (which you haven't shown, but I would urge you to think about having...things like interior lights, 12V appliances, exhaust fans, convenience 12V receptacles...), usually there's a separate fuse/distribution panel that has maybe a 50A line feeding it, often with a master disconnect switch. Sometimes the charger/converter connects to this panel rather than more directly to the battery.
On a trailer with electric brakes, you should have a breakaway switch that turns the brakes on from the trailer battery should the trailer become disconnected from the tow vehicle. This would be powered pretty much directly from the battery. If you already have a setup like this, it presumably has its own battery somewhere, and it would be simplest in my opinion to get rid of this separate battery and use the main trailer battery. (Among other things, doing so would simplify the charge line wiring from the truck.)