Generator supplies 120V AC so fridge should run on AC when in Auto mode.
Check that the outlet fridge is plugged into has AC Power.
If no AC could be due to a tripped GFCI upstream OR a tripped AC circuit breaker
Furnace blowing cold air>>>>>>
Is Fan control on thermostat set to Auto?
Did you select 'Heat' when you turned t-stat temp setting up to 78*F?
Furnace is 12V DC power and propane fired.
Furnace fan comes on and blows air to purge system (makes up a sail switch that allows DC power thru to circuit board)
After purge.......circuit board sends DC to gas valve and spark electrode to ignite flame.
Lack of sparking....no flame
Could be stuck sail switch
Could be dirty contacts on circuit board connector
Could be faulty circuit board
Could be spark electrode not properly gaped or out of position
Post Brand/model of furnace for specifics IF you don't get it working