Thanks in advance!

One thing to consider is that Lithium batteries are tempting targets for thieves and having it sit out on the tongue is not a great idea. You will need to come up with a way to lock it down.

Yes. Usually a LiFePO battery of equal amp/hour rating will have a similar, if not smaller footprint than a lead acid battery.

Or, you could get a Harbor Freight tongue box and install it. Then you can put the battery in there and it will be locked and harder for someone to steal. Not impossible, but even inside it isn't impossible. The goal is to make it more difficult so the thief will go looking for an easier target.

I have a 200AH LiFePO4 battery in a Harbor Freight tongue box bolted to the A frame on our current Cherokee Grey Wolf. I have had no problems with it being there. I did have to drill a hole for the cables (be sure to use a bushing to keep the sharp edges from cutting the wires).

Given the year of your trailer, it may be an auto-sensing converter. Ours is. That means no switches. It will detect and set the charging profile automatically. There is one other issue and that is the ability of the tow vehicle to charge the battery. Modern alternators do not use a fixed voltage regulator, but vary output based on battery charge. Since an LiFePO4 battery will carry a higher charge than the vehicle's starting battery, you may find that the trailer's battery will feed power back to the vehicle and you will leave with a fully charged trailer battery and arrive at your destination with a partially discharged trailer battery. There are ways to mitigate this.

The simplest is to use a diode which allows current to flow from the vehicle to the battery but not the reverse. Couple this with a solenoid which only allows the current to flow when the vehicle is running, and you will be most of the way there. To be able to charge on the move, you may need a DC to DC charger. This takes the tow vehicle power and steps it up to the proper charging voltage for the LiFePO4 battery. If you have solar, you could go with an MPPT solar controller which also has a connector for tow vehcle power. Most trailers go the cheap way with a PWM controller. Mine did. I replaced it with a Renogy controller which had the ability to also get power from the tow vehicle.

https://www.renogy.com/dcc50s-12v-50a-dc-dc-on-board-battery-charger-with-mppt/ - https://www.renogy.com/dcc50s-12v-50a-dc-dc-on-board-battery-charger-with-mppt/

There may be other/better ways to accomplish this, but this is what I chose.