I'm not an Electrician..but...pros and cons

That panel will fit ITE, Siemens, or Murry compatible breakers. It looks like you still have open spaces available, just remember you only need a 30 amp SINGLE pole breaker, and since that second picture is a sub panel, make sure you keep the ground and the neutral on their appropriate bus.

I personally don't think 30 amp is overkill. Especially when trying to run the AC through a small gauge extension cord, I've seen it happen to many times where they melt from the inside out. There's a reason Forest River supplies you with a number 10awg umbilical cord!

You actually base breaker size in a panel on whats available from your feeder breaker. Its a mathematical equation based on the load calculations that are being used by each circuits. So just because you have all 15 amp breakers doesn't mean you can't install a 30 amp.  All of those 15 amp beakers might be feeding outlets that you have nothing plugged into so you have no load on those circuits, or you might have 1500 watt space heaters plugged into all of them and have no available amps (being facetious) .  I'll be honest, whats has me concerned (especially the last question you asked and your own admittance of ignorance) is the knowledge base your working from.  Please be careful and make sure you keep all of your polarities correct if you attempt this installation.

We're glad  you recognize the danger and are proceeding with caution. From your posts and pictures you have a 70 Amp 240 volt feed to the sub panel through that 70A breaker outside. The easiest would be an added 30A single breaker in the garage. If your run is 30-50 feet start with a piece of 2 conductor 10AWG plus ground (3 total). Use 10-2W/G type NM if it will be exposed to sunlight or buried. In the garage box note that all the white wires go to one bus: connect the new white there. All the bare ground wires go to another bus: connect the new bare wire there. The new black wire goes to the new breaker.

For the 30 Amp RV connector refer to this article: http://www.myrv.us/electric/. Follow the guidance for 30 Amp RV service and use an approved outdoor box. With a little help from your friend you'll be fine. If you don't already have one get an inexpensive 3 light outlet tester and test the final installation. You should have one of these testers anyway for campgrounds.

Good luck.

I think an outdoor rated box is overkill in a protected garage.  15 & 20 amp outlets aren't required to be in a weatherproof enclosure in a garage, only that they are GFCI protected (not required for a 30 amp outlet).  Just make sure it is mounted at least as high off the floor as the existing outlets to meet local code.

Found a pretty good video on how to install an RV receptacle at home.