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!