So i'm coming in a little late,but better late then never. Looking at those coils,they looked deformed like from excess heat. For that reason alone,i'd be changing the coils and plugs. The broken tab on the coil plug is an indicator that someone has been in there before. You could probably secure it with a small tie wrap through the plug and around the top of the coil to keep it secure to the coil. I don't like cutting wires and using butt connectors myself, it usually causes more issues down the road. That braided cover is likely from an egr tube running from the exhaust manifold to the intake. As for the issue with the shifter,that's kind of curious. It sounds like the trans range sensor or in old school terms,the neutral safety switch may be out of adjustment or the shift cable is a little out of adjustment. The next time it happens,try holding the shifter tighter towards park and see if it starts then. That would be a good indicator to look at the shift cable adjustment. You could try shifting to neutral and then seeing if it starts as well.
My own misfire experience turned out to be carbon build up in the combustion chamber, or so i'm told. I talked to a bud of mine who is a shop foreman at a Ford dealer. He told me to get the engine stinking hot before trying to crack the plugs loose. I bought the plugs,a can of seafoam, and filled up with Shell premium gas( no ethanol) and drove the truck hard for a few days. My misfire went away and I still have the plugs sitting in my toolbox. Mine is an 07 expy with 270,000 kms. Only in Canada eh!
Keeps us posted,i'm curious what you found.