Hello Avalanche -- and welcome to the Forums!
The owners manual actually mentions a possible way out on the spare tire issue. With dual axle trailers you can remove a flat and tow with only 3 tires on the ground if you keep speeds below 40-45mph. This lets you continue to the next town at least.
Yes, the furnace should work on battery power. Search the forums on 'furnace recall' and read this thread:
http://www.airforums.com/forum...fety-7818.html It would be a good idea to replace the furnace if it is original.
Some of the old friction anti-sway units get in pretty rough shape over the years. The
Equal-i-zer is spoken of very highly in the Forums.
The fridge sounds in pretty rough shape. I like to get away from it all but still find that a majority of my nights are at plug-in sites. This can be one of the more expensive change-outs but will reward you all the time you own. See
www.campingworld.com, search on Dometic. DIY? They're pretty much self contained, but getting it to join with your Argy vent might take some work.
Now that you're hooked I hardly need to say, "Come back often." Enjoy the adventure!