After some research I have found out that the black smudge is actually all the dead pixels. What "killed" them is the LCD being put under tension, not pressure. A drop can cause this. This only happens to AMOLEDs. Hope I helped someone.
You cannot remove the button without removing the glass. Removing the glass is fairly easy, only tools you'll need is a spudger and a heat gun. Tricky part is cleaning the glass or lcd and reattaching them.
First of all, check the current output of the charger. If that value is equal or above the one on the original, then the battery is dead and you should get a new one.
Yes, a loose or partly connected flex could be an issue. This problem should be solved by the third party you mentioned. The fault can only be theirs. No doubt, it's a hardware issue.
