the second issue with the furnace might be because the furnace exhaust openeing might be blocked or something is blocking the smoke to get away - when the smoke starts to "pile up" the furnace will stop working until the smoke is gone
same applies to fires when the smoke cant get away the fire goes off

the first and third issue might be mod related maybe check if there are any remains of mods somewhere in the save files
sorry as i cant dive deeper into that as i prefer playing valheim without mods

did you tried to verify the game files via steam?