The chain fell off the track and now it seems it will only go on backwards - how do I fix this?

make sure nothing is lodged under the tracks this is common things get thrown under the seat and stops them in the track

open gearbox,maybe the gearbox brokeafter the chain fell off

probably the wire fell off one of the Door obstruction sensors
Check the wiring on the little reflector things on the tracks at floor level

You, as the only one of us who can see the bike, need to focus on what is or is not happening to define the problem better. Chains engage gears. If not, maybe the chain fell off. Try web searching "chain fell off" or "chain fell off autobike classic" or any common simple symptom to get a feel for the various reasons it happens.

If it has oil and is not pumping it, then it is probably blocked by a wood chip that fell in to the oil when you opened the cap.
You need to blow it out with air, backwards.

For a chain to come off the track it must be MUCH too loose. The chain should run tight on the track and not hang free at all. As it has been running loose it may well be damaged - and therefore more dangerous than a healthy chain. If I were you, I'd get it checked out professionally. Don't keep trying to use it, as it will overheat and probably damage the track as well.

Modern chainsaws have the ability to run without turning the chain via the chain-brake. To set the brake the uppermost handle is pushed forward (toward the chain) and a firm snap should be heard and felt. To release the brake you pull the same handle back (towards the engine) and get the same "snap".
Concerning oil leakage: Bar/chain lube collects on the inside of the clutch cover and the sawdust mixes with it as you saw. A surprising amount of oil gets absorbed in the sawdust and later seeps back out when the saw is at rest. If the level of oil in the tank noticably drops after sitting overnight you may have a leak...otherwise it's normal.
As for a running chain that wont cut, it is common for chains to be installed backward and the unit still function perfectly (it just won't cut wood). See the proper chain orientation here. In this photo the chain travel is from left to right.

Neither the chain nor the track require lubricant. The roller bearings, the hinges and the rail need lubricated from time to time.

On the rear of the motor unit you will find a control "up force." Increase this about a quarter turn.

Hi my name is Allen!

When the window falls down it is because the cable for the regulator and motor broke. The only fix is a new regulator/motor assembly from the dealership, or a good one from the junk yard if you can find one.

For further asistance you may reach me at FixYa!