I looked up your location on your profile and see your from Alabama, very humid I bet.
I'm going to also assume that your lamp and radio are always outside plugged in, day and night. The first thing I would recommend is that you get rid of both, in those humid conditions and rainy weather, devices not rated for outdoor use will corrode inside, ie sockets, control boards which can lead to a ground fault failure. This is most likely to happen at night from the dew. It doesn't matter if the device is on or off, a ground fault can be caused by water forming a connection between the neutral and ground of your device.
Also since your recepts have been open to the weather for along time you could have corrosion and or moisture inside causing the same failure, I would replace both the front and back recept and install an in-use cover, the new type.
I also think your GFCI breaker is fine, it's doing what it's supposed to, we have very little trouble with GFCI breakers unlike GFCI recepts which fail faster than CFL light bulbs.
I think your Vendo is fine, but you should run an amp check on it to see what it is pulling, you could have a semi-locked up compressor which has a bad spot and only catches occasionally, even it it did lock up your overload should go out before the breaker.