Welcome! I saw your trailer on eBay a couple weeks ago, it looks very clean!
For your year, the second wall switch should be for an interior ceiling light. You probably just have that particular light switched off now- you need to leave it in the on position to use the wall switch. Chances are it's the light over the dinette, I would start there.
The switch for your water pump should be located on the stove hood, along with switches for the exhaust fan and hood light.
Like Tommie said, the battery should go right behind the propane tanks on the front. The brackets are actually designed for a plastic battery box and then the battery goes into that. For basic needs, a deep cycle group 24 battery is what you'll need, along with the correct size box for that. The box should come with a strap to hold it all down to those brackets. Honestly, I'm surprised the dealer didn't set you up with one, or at least suggest it.
I would advise against installing a window A/C. These windows aren't really designed to support one like in a house, and you can't travel with it. There's no good way to seal those to prevent water from entering the trailer, and if you were to install it in a side window, it would make the trailer over the legal width to tow without a permit. Your trailer should already be pre-wired for a rooftop A/C unit which replaces the center roof vent. This would be the safest and most weather-tight option.
As for adding a microwave, your floorplan is a tough one. My suggestion would be to buy a small microwave that can fit in the cabinet right below the stove. This should have enough depth to accommodate one, which I don't think the upper cabinet does. You probably don't have electrical in there, so you'll have to figure out how to run that.
I would also recommend investigating the potential water damage issues. It looks like I see some staining in the flooring by the entry door, and then someone prior added a piece of wood over the floor in the storage compartment. Usually those are signs of significant water damage, which you want to make sure are stopped if not repaired. I'd hate to see you invest a bunch of time and money adding A/C and a microwave if the floor isn't safe.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR