Can I put the exhaust from a bathroom ceiling vent into the furnace vent which is vented out the roof? It is a second story bathroom and it seems there is a furnace duct running along side the bathtub toward the ceiling. Not sure intake or outgoing?
G

No. The fan needs a dedicated duct to the outdoors, as does the furnace.

The furnace exhaust contains, among other things, carbon monoxide gas, which as you should know is a silent killer.

Imagine your bathroom filling up with CO fumes while you sleep.