is the fridge 110 vac or 12vdc ? they make duel voltage units.
imo the thermo electric units aren't worth the "savings" - they run NON stop and don't cool very well.
they only way to power a 110vac appliance is via an DC to AC inverter, or a shore power cord/connection. shore power don't do you any good if you're not parked.
done properly, you'll want to isolate the battery/supply from the engine batteries (to prevent running the engine/starting batteries down) - this is done w/ a ISOLATION relay, which allows the "fridge" battery to be charged when the engine is running, yet isolated the batteries from the engine/start batteries when the engine is turned off.
a microwave cab be a huge wattage drawl - you're gonna need a good size inverter & batteries to run it and you might not be able to run anything else when running the microwave.
i think space in the truck is gonna determine how big a fridge / microwave you have & from there you can determine how large an inverter you'll need.
its no secret that I'm a fan of the EdgeStar, ARB, Engel & Dometic - they're expensive but they work better than any thermoelectric and they'll last a LOT longer - my EdgeStar has been running (non stop) for over 3 years & I have a friend that has one in his van thats been plugged in for over 4 years.