Make the iPhone in Recovery mode and Restore it in iTunes. PS : Don't try to restore it if it has a hardware problem this will surely cause a brick. **Explain more your problem before you do this**
It's not good to a Lithium Battery device to let him without using him. This will decrease the life of battery. So, it's better to buy a battery when you'll need it...
It's absolutely normal that the screen will cost a little expensive. The iPhone 6 isn't an old device it has only 1 year (Apple create a new iPhone every year...) And also, the 6s has approximatively the same components (Except the CPU A9 and other ameliorations)
I "THINK" yes because your 16Gb Logic Board have all the informations about your iPad (Serial Number,IMEI...etc) If you change the logic board no matter with storage because it will change your iPad entirely ! It will be another iPad with other identification...
I had error 4013 with NAND Lines (FindFlashMediaAndKeepOut............... provider<ptr..............) I've changed the screen for my case and it's been working (sometimes the phone starts normally and the digitizer wasn't working)