Post photos and it'll be much easier to answer your questions DD.
I agree with Jan that having to permanently use "stalling" as the method of stopping your engine will be bad long-term. (But I understand your reluctance to have to lift the hood each time too.)
The EDIC relay should sense when your key is turned off and react by getting your EDIC motor to move your EDIC arm to the "fuel off" position. .. (I think you'll probably find your EDIC arm has been removed by your PO to disable your EDIC system. This is what a lot of people do when their EDIC systems develop faults that they don't want to be bothered fixing.)
You have a fuel pump attached to your injector pump and no other "feed pump" should be needed.