Hi,
Most undercabinet microwaves are huge, because they are designed to fit in the huge space above a home 30" range, therefore are 30" wide. Your best microwave for a small space might be a compact microwave from Costco or Best Buy, then build a cabinet for it.
Some 3/4" white laminated wood from Home Depot or Lowes should work well for a project like this, and build a square box that has about 1/2" gap around the microwave for ventilation, then mount the box onto a cabinet already in the RV.
As for installing more 120 volt receptacles - go ahead. They will not draw any current. it is the stuff you plug into those receptacles that draw current, and you are already limited to about 30 amps with the factory installed receptacles, that will not change no matter how many you add. While plugged into the generator, you are limited to about 16 amps at 120 volts.
Your 12 volts is limited by the battery capacity. And that is a balance between battery size and weight. THe larger the battery, and the heavier it is, the more amp hours it will be able to hold. I have a pair of golf cart batteries - 67 pounds each that store 220 amp hours at 12 volts. That is more than enough for a long weekend, even without recharging.
When you plug in the RV to the generator, first thing that comes on will be the converter/charger. It will probably run at maximum amperage for a few minutes to at least surface charge the battery, then slow down the charge rate after about 10 minutes. Running the microwave while the battery charger is putting out 45 amps might not work to well, and might overload the generator, as it is just a little larger than the input of a 1,000 watt output microwave.
1,000 watt output microwave can have a 1,500 to 1,600 input rating. The 45 amp charger putting out 40 amps at 13.5 volts = 540 watts output, probably about 600 watts input. After the charger has run about 15 minutes, or the battery voltage was not to low when started, then you can run the microwave and not overload the 1600 watt generator. It has a 2000 watt surge rating for a maximum of only 30 minutes.
Or look for a 800 watt microwave, with a 1,200 watt input rating.
Be careful of coffee makers and toasters too. Sometimes they can use 1,000 to 1,200 watts, and might overload the generator if both running at the same time.
Most RV's come with at least a 45 amp charger. That is plenty for most uses, and will recharge the battery in a couple of hours. It is best to split up your generator run time - if practical. I would run it about 1 hour in the morning and 1 near sunset if I had your set up, because the charger will put out the most amps the first hour, then taper to a slow charge after that.
Best described as a frog jumping towards the end of a log. The charger can put in a lot of amps to a battery that is at 11.7 volts, then less amperage to a 12.5 volt battery, and takes a long time to add a few amp hours to a battery more than 80% full. Just like a frog jumping towards the end of a log, it can leap a long ways at first, but must take smaller jumps as it gets closer to the end, as it is not jumping off, just to the end.
Good luck on your project.
Fred.