Hi, Munky. Long post warning!!
Let me start with I am an electrical engineer with 28 years experience, some of that in the satellite power converter industry. I have said the following before and been ignored by others, but will say it again in greater detail and maybe be believed. I do know what I am talking about, but there are those who will offer advice to the contrary. They may be well intentioned but I would not follow their advice for my own trailer and recommend you don't either. Time is much too precious to spend it on a bad idea.
Paralleling 12V batteries will indeed give you 12V. That is not a problem.
Paralleling two 12V batteries is OK, but not optimal. What happens is that imbalances develop between the batteries over time. It does not take very long; just a few charge/discharge cycles and their full-charge voltage will differ significantly. As imbalences develop, even when not under load, the stronger battery will attempt to charge the weaker battery. This charging of one battery by another leads to premature failure of both batteries because you end up with some batteries constantly being charged while others are being discharged. When a battery ultimately fails it looks like a resistance to the other batteries. They see a load, even when everything is off. You respond by charging the batteries more frequently, and the frequent charge cycles lead to failure of the good batteries.
The more batteries you parallel the worse the situation becomes. One battery fails and the others fail in cascade.
There are several ways to deal with this:
1) use a single monstrous battery
2) string your batteries in series and use a down-converter to give you 12V
3) Install a series diode between each battery and the load. Unfortunately this requires a separate charger for each battery, or you have to move the charger from battery to battery to charge each individually.
4) parallel a bunch of batteries and live with premature failure.
5) use two 6V batteries in series, three 4V, or six 2V.
#4 is, in my view, the least desirable and most expensive alternative because you will be buying a lot of batteries. If you only have a few batteries, #3 may work for you. #2 can be pretty good, as you can readily get 72V to 12V converters. Vicor is one maker. That allows you to string 6 batteries in series, but a charger for this arrangement will cost you. #5 is best if you only need two batteries. Batteries are strung in series all the time with no evil consequences.
Frankly, by the time you buy batteries to run AC all night you could get a nice little Honda genny to do the same thing and save about 300 pounds.
I apologize for the long post. I seem to do that, but I wanted to point out some of the alternatives as well as the problems. As another TTT nut says, build what you want and be happy with it.
Oh, yeah, you had other questions -
A bunch of batteries in parallel will not hurt your inverter or charger.
Choose your charger to give you a charge rate about 1/10 of the capacity of your battery. IOW, if your battery is capable of 100AH, you need a 10A charger. +or- 50% or so. It's very inexact. A high quality fast charger will allow you to charge at a faster rate, up to 50% of capacity, with corresponding potential reduction in battery life if it is not a really smart charger. With all those batteries, get a really good charger. Or plan on buying lots of replacement batteries soon
Have fun,
Sherman
In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away.
-- Antoine de Saint-Exupery