The clicking noise is probably the electronic igniter trying to light the propane flame.
Turn the fridge off. Make sure the main valve is open on your propane tank and that there is propane in the tank. Light the stove cook top to make sure your lines are purged of air and that the system has pressure. On high the burner flame should be large and vigorous. Turn on the fridge...turn it to gas operation and turn the temp to coldest setting. You should start hearing that clicking noise again. It will try to light for several seconds and if no flame it will time out. The line may be full of air so you may need to turn the fridge off and back on to get it to cycle again to get gas to the burner. The newer ones will cycle several times on their own. If after several tries there is no flame, make sure the manual shut off valve on the back of the frige is turned on.
The lights going dim to bright continously while on generator could be caused by rpm fluctuations of the generator. Does it sound smooth? Have you checked the water in the batteries? Check the voltage at the batteries with a multimeter while that light fluctuation thing is going on.
If you can't figure it out, go camp a night in a good campground. Early in the morning open all the hatches, spread your tools around in sight and an old guy will come by and ask you whats up. He will get you dialed in.