It should work. Score and snap is fine for Durock and other similar gray mesh-backed cement boards, but doesn't work that great with Hardie Backer and its clones. You'll trash your blade, but it should cut. Might be bad for the saw itself, but a few cuts shouldn't kill it.

I use an angle grinder with a diamond wheel for this kind of thing if I'm being serious about it. You can also use a jab saw, like for sheet rock, on Durock, but not Hardie Backer.

That's pretty normal. Replacing the affected sheet rock is how it's always gone on the job for me.

Anything wrong with good old thin-set mortar? It's more work, but it's not super hard. With the quantities you're using, you could easily mix it with a stick or a common power drill. And it wouldn't have any of the problems you're worrying about.

America has plenty of women who would be happy to do the housewife thing. Just don't expect her to have a job AND do housewife stuff, and discuss your hopes and expectations before you get too serious to be sure you both want the same thing.

Normal Nut November is over, now I get to continue masturbating normally as I have been the entire time.

I think that a new hole through the floor or bottom plate of the wall is the solution. A 4" hole in a 2x6 bottom plate is no biggie, just needs nail plates. A 4" hole in a 2x6 stud ranges from sort-of-harmless to an imminent structural danger depending on why that wall uses 2x6 studs instead of 2x4. If they're thick for load bearing, you'd risk a collapse of some sort. If they're thick to contain plumbing and pipes, it's sketchy and inadvisable but viable in a pinch. Be very cautious with your assumptions here.

Ideally, your large pipes go straight up or down within walls. And in floors or ceilings, they should go between joists unless they can cross over in the attic or under in the basement.

You'll want to use a material which has similar properties to the column or stronger. Nothing wrong with a metal plate, but if the columns are PT lumber, then a PT shim should be OK. Wood does compress more across the grain than along it, but not by enough to be a big deal in a deck. Cedar is also pretty rot-resistant. If you've got an inspector coming around, the metal plate others have suggested may be better, if for nothing else than because it looks like you took it seriously. But the way to actually take it seriously is to replace the column.

I don't have a clear vision of exactly what's too short here, but it sounds a lot like it could be solvable with a cedar shim shingle or a carefully cut piece of PT wood, jammed into the gap. Not sure what the inspector would think of that, but it'll bear a load okay. The holistic solution is probably to cut the bracket off with a sawzall and cut a new post of the correct length, then install a new bracket.

There are waterproofing agents you can spray on the grout that will do a much better job of what you're trying to achieve without as much work, but I think the real problem is how much water you're spilling on your floor. That doesn't seem normal. A floor designed to catch and hold that much water on a regular basis would be pretty special.

Looks doable. Make sure any framing that touches the concrete is pressure treated and you should more or less be good to go. Getting a garage door to sit under a slanted roof might be a bitch but it should be possible.