I don't think the car has a factory immobiliser, but Learoy has a schematic for a '92 which implies that it does -- at least for that year. But you can see for yourself. Lock the car, reach-in and open the door to trigger the factory alarm, and then try to start the car.

Your driver-side window switch is faulty. Here is how the switch works. There are two wires from the switch to the controller. When you press the switch to raise, one of the wires is grounded. When you press the switch to lower, the other wire is grounded. And when you press the switch past the detent to use the one-touch down feature, both wires are grounded. Your problem is that in this last instance your switch is only grounding one of the wires, and the controller gets a signal to raise. A replacement should be inexpensive, but if you like you can disassemble the old one and clean the internal contacts to restore its functionality.

If the passenger window does not go down automatically, I think it could be the switch in the bottom of the door is stuck closed and is signalling the controller that the window is already down. You can test this possibility by seeing if the one-touch down feature works when the window won't lower. I don't know for a fact, but I suspect it relies on the same switch in the bottom of the door to let the controller know when the window is lowered.