I'm guessing it's easier to strip out the entire corner. Scrape off as much loose stuff and old mud as you can, then retape. I use paper tape but you could look into "drywall inside corner bead" for alternatives. I also have a corner trowel which does a great job, but the expense and learning curve have me giving only a qualified recommendation for that.

I flick a wet brush into a towel so any liquid goes, then rub the brush with the towel while bending the bristles. Also I like a damp brush, so I wet it before starting to paint.

A mini roller is my preferred tool for sample testing. A brush messes up the texture.

If a drain pipe won't loosen, and is still solid (not falling apart from rust), one fix is to cut the end off, removing any stuck nut or fitting. Then use a rubber coupling, or "fernco" to join the sink drain to the wall pipe. A hacksaw would be sufficient cut the pipe, but I'd use a sawzall cause I have one and they make quick work of it.

Rusted steel drains really don't want to come apart, even when standing and jumping on the pipe wrench. So my usual approach is to cut the pipe, and attach PVC with a fernco.

People who have never tried it will assume that a slab door is easier than installing a prehung. Experience shows the opposite is true. A slab (bare door) is cheaper for the initial purchase, but is more difficult to install, and requires additional tools, plus hinges, and way more fussing about.

Search for "slab or prehung door reddit" if you care to see how other redditors have discussed this.

Toilet flush handles are reverse threaded so they don't loosen up with each flush, which is a counterclockwise turning. Instead they tend to snug up if anything because of the reverse thread. This is due to the standard handle placement on the front right of the tank.

That is likely reverse threaded. Try turning it the other way.

Use whatever you've got that will fit with the box, any scrap. I'd give it a try, and if that bit doesn't work out I'd consider picking up a new set of drill bits at the big smock store, with sales ramping up right now.

To get a clean hole I would try using a piece of wood as backing while drilling.