These are typically independent appliances so the problems may all be unrelated if you have confirmed the basics of 110AC, 12DC (lights) and propane.
I did some searching and seems Colman sold those with Norcold or Dometic fridges. Which brand did yours come with? Here is the owners manual for the Dometic http://bryantrv.com/docs2/docs/rm2193.pdf
It has lighting instructions and some trouble shooting/maintenance tips. You say the fridge does not work on 110, 12v or propane. Does the piping in the rear of the unit heat up at all? You might want to limit your troubleshooting to one source at a time. For example, on propane, do you get a flame? I recently added an entry to the POPup section of this forum on getting my fridge working on propane.
The furnace should have a wall mounted thermostat. There is a switch on the bottom of the thermostat that has to be on. There is also a breaker switch under the front cover of the furnace that has to be on. Of course there is a fuse in you power converter that should be checked as well. Once all three are okay, turn up the thermostat to force the furnace to fire up. The furnace fan will start first, then you should hear the electronic ignition spark a number of times to light the furnace. If it does not light after the third try it will pause for about a minute (with the fan continuing to run) and try again. If you have no fan operation, it is time to check for 12 volts. If you have fan, but no spark sound I can provide some more troubleshooting from previous experience.
At the first of the season both of these appliances take some time to light because it takes awhile for the propane to get through the pipes. My inside stove connection is next to these appliances so I typically connect my stove inside to purge the air out of the lines. Once it lights the others light more easily. (The fridge uses so little gas, it would take forever to purge the air out of the main propane line)
I do not have hot water so I cannot help much there.
Please provide a bit more detail on what you have tried and what results you saw or noticed.
The trailer will be more enjoyable when everything is working.