Electrical requirements

Many trailers are out there using the original wiring and inlet.If you are careful, yes, it can be done. Inspect the inlet carefully for burn marks and toasty wiring. I've had good luck with original wiring in all but the oldest trailers. (53 Hanson had knobs and tubes) If the light fixtures were used with reasonable sized bulbs, that wiring is often OK as well. 100 watt light bulbs tend to fry the wiring, so check the connections.

I always rewire for 30 amps, even it the 15 amp inlet remains. It makes it much easier to upgrade later to have the wiring in place. The general "rule of thumb" for total amps is less than twice the incoming amperage. 30 x 2 = 60, so about 55 amps total.

Examples:

Circuit 1: 15 amps, this is the original 14/2 wiring, usually lights and an outlet or two
Circuit 2: 15 amps, new outlets. This could run the dorm fridge and a small battery maintainer, maybe an outlet on the closet, etc.
Circuit 3: 20 amps, at least one outlet in the kitchen area, an outside outlet. Since this will be used for a kitchen appliance, you want to run one item at a time.

You could have two 20 amp circuits and one 15 as long as the wiring is the proper gauge.

While you could run the A/C thru the trailer system, the easiest way to power it is with it's own cord. Totally bypass the trailer, allowing the A/C and microwave to be used at the same time... if the Campground breaker will take it.

Keep in mind Campgrounds can have poor quality outlets and less amperage than advertised. Many of the outlets have been yanked, twisted and abused. The contacts actually arc even when plugged in, some have reverse polarity and/or trip the breaker continually. Inspect the power source before plugging the trailer in.