One possible cause is coolant temp sensor or the plug dirty or disconnected. High resistance tells ecu to add gas for a cold engine, low resistance to subtract. Check plug and sensor contacts, read sensor resistance with ohm meter if available. Or scan the car looking for engine temp to go low to hi...

Can you remove plug and see if side electrode is bent to touch center, post a pic also?

From your post I am going to presume that the high voltage side is failing. That indicates excessive load which leads to the condition of spark plug. The ceramic insulator needs to be clean, also gap should be proper (unrelated however to the water puddle event). Then I'd check the corresponding gro...

The piezoelectric crystal is cut such that it favors the frequency of interest. Similar to the quartz crystal used in radio oscillators. The crystal does resonate on multiple frequencies but the dominant is several orders of magnitude higher.

Fuel inj relay is in engine bay electrical box, driver side. I'm thinking the immobilizer shuts down relay.

+1 on air leak, also wondering if there's a way to see actual fuel trim levels and also test the TB.

Sounds like relay FMA2 or fuel inj relay shuts off and cuts power to injectors. ECU controls that. Can you lock/unlock car with your key fob?

I'd repair or replace the cv joint as it may cause the vibration you mention. Since you removed the prop shaft the read diff, or bevel gear, should not make noise as there's no load on it. And you noticed noise coming from front. Motor mounts is also a good suggestion after hitting a curb.

Several things going on here: there's this overload relay that monitors current for the pump, so when car quits you can check volts on blue/red wire that powers relay contact. Then, there's the relay coil voltage on yel/gray wire coming from ecu which can be checked when engine quits. Fuse for pump ...

There's an overload relay #2 in the electrical box where the fuse #2 is for fuel pump. The circuit also powers central locking, so see if that works when car quits.