That's a 10 amp converter, 120-125 watts max output, probably not designed to serve as a charger. You have two 7.5 amp circuits, 90 watts max, each. The low capacity of your 12V system is why the hookup lines ate so lightweight.
You are probably going to have to charge the battery with a separate charger. The switching suggests this.
I don't know the capacity of that battery, but I do know that a small number of low-wattage 12v bulbs, like parking and tail lights, can run a starting battery down overnight.
Your loads other than lighting?
Phone charger, probably OK, as the 12v adapters draw 0.5 to a little over 1 amp (double that for a 2 USB).
Laptop, problematic. I have power bricks for laptops ranging in size 75 watts to 200 watts. The smallest is thus close to the max capacity of one of your 90 watt circuits.
Cooking appliances: my crockpot needs 200 watts, rice cooker 500 watts, teakettle 1000 watts (though the one in my RV may be slightly smaller). Even if you could find 12V DC -> 120 V AC inverters of appropriate size, you don't have the capacity on 12V side for anything larger than 75 watts at 120V.
For using electrical appliances, think in terms of needing a 120V hookup. You might have a single 15 amp or 20 amp AC outlet for this, otherwise you will be running an extension cord inside from the power pedestal. Or from a camping generator, which range in size from 500 watts to more than 4 KW.
Your 10 foot Eagle is functionally a tent up off the ground, with some lighting circuits for convenience. So not a house on wheels, rather something for camping. Most of your heat/energy will be coming from fire, rather than electricity: campstoves, lantens, campfires, bbq pits, gas grills. Modest electric lighting is possible, with additonal stored energy, e.g. battery powered LED or fluorescent lanterns.
Making a tent camper of that vintage serve as a self contained house on wheels is going to take some upgrading, which might start with electrical systems.
Tom Test
Itasca Spirit 29B