It's important to note that the Parthenon didn't degrade slowly over time, and crumbled out of neglect. It was actively blown up. OK it might have been already degraded when it was blown up, but it was still a structure intact enough to store munitions. Then the Venetians lobbed a bomb that ignited the munitions and Kaboom... no more Parthenon.

Today it's parts are being cataloged and when possible, reassembled. SOME of the parts are in museums around the world, so to fully reassemble the parts would require taking them out of museums and placing them back into unprotected open air... an untenable idea for museums, or would require manufacturing new replica parts, which has been done in a few cases.

Swimming can help as long as water is cooler than your normal body temperature.

If it's 100 degress F and the water is 90 degrees F you'll still overheat and die.

I'd drill it out and retap the hole to use a bigger screw. Rent a tap and die set from an auto parts store.

Failing that, I'd drill it out, and then replace the valve and handle with a new one. Just leave the mixer housing where it is.

Yes, that should have been installed with the garage door. But that's an old door, so yes, install it.

Hole in the roof, call that roofer even if to do a temporary patch. Water is collecting above the vapor barrier, Punching a hole trough the vapor barrier makes matters worse by allowing ceiling plaster to get wetter faster. You'll also need someone who can repair vapor barrier and plaster, and possibly even attic insulation.