Did I Pull the Battery Adhesive Correctly?

Trying to remove the battery adhesive. I pulled the papery stuff under the recycle symbol on the battery. The bottom of the sticky paper is not white though. Only black. There is also a black piece under it that is not feeling as papery and is lifting up. Under that part that sticks up I can see two silver rectangles that I am unable to photograph due to me needing both hands to show it. Did I puncture the battery and pull the wrong part? It kind of smelt like nail polish for a few seconds. Is that the battery burning or is it just the adhesive I am smelling?

Update: I think i got scammed when i initially bought my phone! I ended up prying the battery off with my bank card. Underneath it was a blue film, and two strips of white adhesive not going along the battery vertically but instead horizonal. I dont think it even had the adhesive strips it was supposed to have? From my understanding I bought my phone new not refurbished.

Anyway any advice if I may have inhaled a toxic gas? Is this harmless? What symptoms should I look out for? Can a damaged battery still be recycled? How do I prevent this from catching fire and or gassing up the place? I have a fireproof box, will that be effective storage? If i cant recycle it, how else do I dispose of it?

Update 2: Found a loose screw near the bottom of the phone. All screws removed have been accounted for. Noticed a screw was missing from the homescreen piece. Screwed it in with no resistance...Phone has likely been opened before and then proceeded to not be screwed back correctly.

Also the little black lasso from the camera piece metal plate is non existent. Dealing with so many blows right now. I hope whoever worked on this phone before me did not make this a dangerous device. I hope these mishaps arent important because wow.