I had a iPhone 5 that had a bad battery and started to bootloop so it may be the battery also and in other to go in dfu u need to plug phone to computer then shut it off and I'll tell you the way I found to put the phone in dfu mode after its connected to computer and it's off press and hold power and home till the apple logo goes away release the power button but just keep holding down the home button till your computer makes a noise and says found phone in dfu mode. FYI I have a extra iPhone 5s battery from a phone I bought for the screen.
I fix laptops and I never came across a laptop that won't power on with battery and with AC plugged in but using common sense first thing I'll do is check motherboard where power supply is at and look for a cracked solder joint or loose connection
This is the connection that gets lose when putting in the top metal screen just push on it till you hear it click in place it has to click in place I have make the mistake of putting it on and seems like its connected put never hear it click so I found out it clicks when it sits correctly
Your LCS ribbon (plug) isn't clipped on correctly to the board you need to push down till it clips on then slowly and carefully close the screen. This is a bit tricky to do because when you lift to put the screw on top everyone makes the mistake of lifting the screen to give you clearance to put the tinny screw on the top metal shield and by lifting you unclipped the LCD plug which the metal holds in place and not getting good connection.
You can move apps data to SD card by going to the settings/app then click on the app you want to move and in the app settings screen that pops up you will see a move to SD card button go ahead and push move to SD card. It will let you move downloaded apps to the SD card if its gray then you can't move that app
Okay let me try and get this straight your trying to pretty much have your sound system play straight off your phone but you don't have a amp to power full range speakers well now this is where I'm confused are you using the cars radio aux to play from your phone or are you trying to bypass the radio? Once you clear that out for me I'll tell know the answer to your question
You can go to Device Manager than under Network Adaptors see if you have any drivers installed and if you do right click on each and see if any are disabled. On the start menu search type Device Manager then follow the steps I mentioned hope this helps