Welcome to the forum.  Just wanted to let you know that you are replying to a thread that is 3 years old.  Not a big deal, just wanted to let you know in case you didn't get a response from the OP.

Clearly the alternator isn't working and its possible that could be causing some or all of the issues preventing the engine from running when the battery drops too low.   Those codes would not prevent it from running.   Is the power to the coils with just the ignition ON ?

Thanks for your reply, I am using Forscan, the PCM self-test with the ignition key ON and engine OFF would be good but it does not go too far as it encounters problem with the IAT (Intake Ambient temperature)...let me check into that.  For the alternator it is a rebuilt one, not an OEM.  For now my question would be: what can cause a no-spark condition at an individual spark plug if the individual ignition coil is good?              

I would start by scanning for codes using Forscan.   Where did you get the replacement alternator? - its widely reported that non-OEM alternators or rebuilt alternators don't work and the voltage at 12.2 confirms that.

I changed the 3.5l  using a  2010 engine installed into a 2010 ford Edge, I re-used my wiring harnesses, I fixed 3 coils connectors (due to locking tab broken), i fixed 1 camshaft position connector (due to locking not working, I removed and re-inserted the sensor).  The engine started a few times for a few minutes and died suddenly and softly (no noise or explosion!).  Now I cannot start it anymore, I pulled out one spark plug and I have no spark when I ground the bottom electrode.    When the engine dies the battery voltage is around 12.2 volts, the alternator is new and my Dewalt battery charger says the alternator is good.  Any idea?  When the engine ran for a few minutes it was always smooth and quiet, not rough or noisy (I had a big smile on my face that vanished when it died!)  

Well it isn't the FCIM. It did it again. BCM maybe? And then every other connection in the car? What a let down this purchase was. I wish I could afford a new car.

Anyone have Forscan that can take a quick datalog and send it to me? Just trying to get a “control” log to compare from another Edge Sport. Can be stock or tuned. This would be extremely helpful. I can send you the list of pids to log. 

Carfax shows "Status: Remedy Not Yet Available".   Could it be that the local Ford parts department has stock of the old hoses?    

I tried to schedule an appointment for the brake hose replacement on my 2015 Edge 2 months ago and the dealer said they had not gotten approval from Ford to do the work. I called the parts dept. just to see if they had the new hoses and was told they had them in stock. What's going on here? Has anyone else had this problem getting the rear brake hoses replaced?  

Late to the party, ended up here because of a P0480 code related to the Cooling Fan 1 Circuit being shot. My fix ended up being bad connectors, only really been able to find these one place (linked below). I spliced in 3 new connectors and was GTG.   https://www.ebay.com/itm/318672639358