This also helps hide the seam between cemented board and drywall which isn’t always perfect.

If they are clogged you might need a sediment filter/screen on the incoming water line or after the pump.

Is it a self priming pump? If not you might have to go through some sort of priming procedure. Although my guess is the pump isn’t, or at least wasn’t the issue.

I would think even with a vent clog you would get some pressure at first and then it would drop off. And different faucets having different pressure indicates to me it’s probably not the pump or vent.

I suspect the faucets inlets are clogged. To check the inlets of the faucet lines turn off water and remove the lines between the wall valve and where they connect to the faucet. There are usually screens that can clog up and kill the flow.

Dehumidifier will work but only if you drop the humidity level far enough in the house which is miserable yo live in. But like you said that completely goes against the whole point of adding humidity in the house for comfort. Even high end windows can suffer from this when temps drop. Generally double hung windows get it worse than casement windows.

One thing that can help is to get air movement against the windows. If you have curtains keep them closed at night but open them for a while during the day and see if it helps clear it up. Otherwise a quick wipe with a towel is the quick solution.

Is it a tub with a shower or just a tub? I’m wonderful you accidentally bent the actuator to turn the shower on and it’s partially stuck between tub and shower mode? If that’s not it is there an old linkage with a lever somewhere that used to activate the drain stopper?

If you haven’t flushed the water heater in several years probably better to just leave it as is. Some risk

Could it be done correctly…most likely. You should absolutely consult with a structural engineer to make sure that joist can be modified in that area.