lol, very sure the phone has been fried. a board problem. it be caused by the car charger. playing with phone while its on charger stresses the board alot with much current flowing.

i'm sure it's bad Battery. the only way to rule that out is if the batteries can perform well from another iPhone. until then get original Battery. there are way too much fake Battery in markets

don't be scared, you only have one problem and that is your battery. get a replacement battery then come back and update me.

there is adhesive that comes with it which can be pull after heat up hot air. but you will need to look for good adhesive to glue it back. otherwise it will be really ugly. i would advice you find the complete front panel

first of all. plug the iPhone to PC. check if it's recognized by iTunes. if iTunes can see it then download itools to your PC. and see if there is display from the mirror in itools. work around the iPhone screen if the touch is responding. let us know after that.

you have said so much but you haven't said anything. Edited: after going through your post again and again, i think i understand what you mean. if i get you correctly is that the battery don't last long. ?? if the logic board is not over heating and the phone is not hanging up, then there is no way the battery can drain really fast. so for this reason i will suspect that the fault is from the battery. for the display test charge to 100% step 1. let it stay idle/sleep for 3 hours with airplane mode, turn off all background running app. off wifi. then check how many % drop. charge again to 100% step 2. remove display from logic board. power it on without display. let it on for 3 hours. but back the display and then check how many % drop. i guess you will figure that out. from battery problem from there you can figure it out.

one last thing to do before you dump the phone. soaked the logic board inside soap water for 6 hours. after that wash every part of it with soft tooth brush with the soap water. then rinse with clean fresh water properly and dried in the sun for 12 hours. then tried powering it if it work. check my summary. thanks

have you check if you can switch it off and then switch on again from power button while it's charging? if yes than sign of battery... but if no sign of power button.