It seems to me that neither you nor the current owner has a good handle on what this trailer has and what it doesn't. Since it's so far away and you're not able to take the extra drive out there to review these issues it might behoove you to research a local Certified RV Tech and have them do a pre-sale inspection. They will easily find out the answer to all of these issues such as battery, tires, etc. If it's that new I doubt you have any worries about tires but once I got it home I would go through the braking system and bearings, etc. but that's just me.
Oh, if it came with a residential fridge it has an inverter somewhere but if it didn't come with a residential fridge, I doubt it has an inverter. Especially since it sounds like the current owners purchased it for a specific purpose knowing it would remain connected to services and not as a "travel trailer".
Good luck!