Great question — answering as the UphillTech team:
All of these questions are moot until you correctly identify what caused the drywall to get wet and that is corrected. Drywall does not just get wet on it's own. Once the water source is found and repaired, you can go about with drywall repair. The insulation is probably just for sound abatement around the P-trap and drain pipe. It really doesn't matter to have insulation between an upper and lower floor. The wood shows signs of water intrusion, so there is more proof that something has allowed water to get there. Just add a couple of screws to anchor the drywall to the wood. Here is a video to explain how to do a drywall patch. Using wood to back a drywall patch . The video tell you about...
Full answer by RMDman: https://diy.stackexchange.com/a/330009 (CC BY-SA 4.0).
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