Do you have the outside temp display next to the time at the top of the home screen?
If so then you might have a flaky APIM that drained the battery. If the MFT problems reoccur take it back to the dealer.
Locking it shouldn't make any difference.
It's not offered by Ford - that's just the dealer trying to make a bunch of profit. Skip it and save your money. You can get a professional detailer to do the same treatment with better products for half the price.
I would think this was due to the pending software rewrite. Now that the software is out of the way they should be more open to continued problems especially if it sounds like a simple hardware swap.
You should be able to get the current owner's manual/MFT guide at www.motorcraftservice.com -> owner guides. If it doesn't work for your 2011 try a 2013 model.
A package has to be developed that the dealers can sell and install and the software to do that has to be developed/distributed. Assuming Ford wants to be in that business.
My guess would be that the belt is slipping when cold. I think if it was the alternator it would happen all the time. See if the dealer will change the belt. You may need to leave it with them overnight.
Your MAF sensor is incorrect. Get it fixed with the intake or put it back to stock. The intake mfr should be able to help. If not then you bought the wrong one.
That light indicates a problem with the charging system - could be the serpentine belt or the alternator. Does not sound like the battery if it's cranking ok.
There is nothing you can do about it. Only the dealer can reset or replace it. You can try removing the HIDs but I'm sure the dealer has seen this problem before.
You fried the smart junction box. It might just need to be reset, otherwise it needs to be replaced. And if so don't expect the warranty to cover it, even if you have "tons" due to the HIDs.