Can a portable space heater designed to connect to a 100lbs. Propane tank be connected to a feed from an external 250 gallon propane tank? The non-working furnace has a feed from the 250 gal tank that I would like to tap into. Is this possible? Is it safe?

Yes it is possible but all the pipe work has to be done to code for safety reasons. In other words all the fittings and pipe have to be approved for usage with propane and all the pieces need to be assembled professionally to prevent leaks. You will also need to check for proper pressure regulator attachment/usage. Many outside tanks have a tank regulator and a separate house regulator along with a built in pressure regulator on the heater itself.