We have one of these in our shower. Works fine. I believe it needs to be screwed into studs though, so the framing behind the cement board would need to be in the right place for the bench.

Some pedophile read this and thought, "yeah!"

I don't know shit about fuck, but it I don't think a shop vac is gonna clear water out of the line. If it were me, I'd cut off water, open the spigot, and also open some other tap further up the line. Then I'd jam a blower nozzle on a compressor into the spigot and blow the water back up the pipe. Maybe wrap some duct tape around the nozzle to get a bit more oomph on it.

I bet if you braced the column with a bunch of 4x4's, you could push on it with the excavator to straighten it up. The 4x4's would help spread the the load over the height of the column.

Then again, you might just collapse the whole thing, since I'd bet that things hollow. But then OP could do a follow up question about DIY brick laying.

I know this is posted under DIY, but we've had a fiberglass repairman fix some cracks for us and they're perfect. Can't even tell a repair was made in that spot. It's a fairly quick fix, so I doubt it'd be excessively expensive.

Ah, I was thinking you'd have a pump in the external sump.

But yeah, ultimately I think the answer to your question is going to be pretty specific to your situation. It's going to come down to how much water there is and how permeable the surrounding soil is. Probably no real way to know that other than either hiring an engineer or just building it and seeing if it works.

Kinda depends on the specifics of the situation. If your external sump was below the elevation of the bottom of your basement, and water could flow relatively easily to the sump, then it ought to be able to keep your basement dry (assuming the sump could keep up with the volume to keep the water table suppressed in that area). There's also the question of where the stump is pumping to...

This is more or less what I did for my 10x16 shed, but I'd argue the gravel doesn't need to be that deep, and you don't need to bother with the different gravel types. Just get a couple yards of 3/4 crush, nestle some pavers in, level them as best you can, and call it good. If the shed settles a bit (which it will), the worst case scenario is that the doors stick. When that happens, jack up the corner that settled with a floor jack, stick some plastic shims on top of the pavers, and drop it back down. It's a 5 minute fix.