sounds like damage to your battery i would open up you phone and check if its burst or if there is any other damage if so either change your battery or take it to a phone repair shop to be checked over
The "black sheet" is your lcd well half of it anyway if your not very experianced you should always order the lcd+ digitiser as it makes the repair so much easier
You really dont need to change it to be honest but if you do any hard drive that you can connect via a pcie port should work as long as its mac compatible. Just in case you dont know what a fusion drive is its a 128gb SSD linked to a 1tb Hard drive in a special arrangement giving you a good balance between speed and storage space
You should be able to connect it to a computer and download that data off of the phone if not you will just have to save up for the repair If it uses a micro sd card for memory then your data should be on that so just put it into a computer or another phone
There are a few different things it could be your lcd could be gone or your battery or logic board you would need to take it to a repair shop to be examined before anyone can get to the bottom