I have done searches already on this site and others and I cannot seem to get answers to my questions.  I have also looked at maccwall's website and some others that are linked on here.  Everyone has such helpful information.  I bought a used Cherokee trailer that has a Carrier AirV a/c installed.  The trailer also has a deep cycle battery and a breaker box with two 15 amp breakers.  There is a standard household receptacle on each side of the trailer with two outlets.  The Carrier website states that this a/c is required to have a 20 amp circuit breaker.  It did not come with a power cord, but I found a 30 amp cord on CampingWorld.com. 

1.  Is this setup enough to run the air conditioner as well as a compact fridge and maybe a radio? 

2.  Should I be concerned that the a/c is not on a 20 amp breaker? 

3.  If I hook up the 30 amp cord to a 15 amp adapter and plug it into a household outlet, is this enough to just run the a/c?  The specs on the a/c say that it only uses a full-load of 12.9 amps to cool. 

4.  Should I be worried that there are no fuses? 

5.  Has anyone found a good book or website that gives basic eletrical information that is easy to understand? 

Most household circuits ( for 110volts) are 15 or 20 amp.  Depending on who and when the house was built. With the cost of electrical wire now at $50+ a roll, More and more builders are using 14 gauge wire to most of the electrical outlets and only use 12 guage where they have to , Usually the Kitchen, Bathroom and garage.

So IF you plug your 30amp cord into an outlet serviced by 14gauge house wire you will only get 15 amps. And  that probably won't run your A/C unit. You will need a 20amp service, especially if ANY thing else is turned on. Go look at your circuit breaker panel and see what size breaker you have in the panel for that outlet.  If the house plug you are plugging into is not powerfull enough, It doesn't matter what your trailer is wired for, You will pop breakers in the house instead of in trailer.

This is also true for generators.  Most generators have the standard twin outlet plug for 110volt. This outlet on most generators is 15 amp. On larger generators, they have the standard twin outlet at 15 amps and a RV outlet. (Round with 4 prongs) at  30amp 110volt.

Most RV's come with either a 30Amp Service or a 50Amp service. Horse Trailers usually being on the lighter side of the RV world usually have the 30amp service.  What this means is your Trailer is set up to Accept 30amps of 110volt current as a power source.  Your panel breaks this 30amps down into various circuits. The two 15amp breakers in your trailer service lights, outlets, possibly a electric water heater, or the fan on your heater. Also out of that main panel they usually connect the battery charger, and A/C unit. Depending on the unit these may or may not be on breakers.

To anser your Questions

#1 A 30 amp service is adequet to run your trailer. But a 30amp service in your trailer can not "Magically Boost" a 15 amp power source.  So if you plug into a 15 amp plug, thats all the power your trailer will have.

#2 No

#3 Your specs say you need 12.9 amps.  A 15 amp breaker gives 15 amps, So you are ok, You jut can not turn on your Microwave, TV and DVD at the same time.

#4 No, That's why you have breakers.

#5   I wish!   but you might try RV.net  Serveral forums that deal with trouble shooting RV's and Trailers