Blue painters tape is only guaranteed to not mess anything up if removed within 7 days. When she removes that wallpaper, the walls will be destroyed no different than if she glued the wallpaper properly.

Sorry but I disagree about the water from personal experience painting with a dry brush versus one after I washed it. Especially on ceilings, you get diluted paint running out of the ferrule and it makes a mess. When it's wet, it thins the paint, lowering the viscosity. I can use a dry brush all day and not get paint to the ferrule. Use a wet one for an hour or two, and it does. And it's worse with epoxies and solvent based paints. You can see for yourself with a little experiment. Take two similar brushes and wet one of them. Put a 1/2" of paint in a cut pot. Set the brushes in the cut pot and walk away for an hour. When you come back, you'll see the wet bristles have paint bleeding up the bristles well above the line it was submerged to, while the dry one won't.

Looking around on Google, it's a mix of some saying you should, and others saying don't do it. It depends on which source you look at. Neither Sherwin Williams nor Purdy recommend it, but I see people on quora and other places saying you should. So I'm gonna go with the guys who make the brushes instead of of randoms on the internet. Nothing against you if it works for you, but I just imagine a person who's not a pro painter making more of a mess with a wet brush. And all the sources that do recommend it say it is too help with cleanup. Other sources say it's bad because it dilutes the paint. So I wouldn't recommend to the average home owner.

It can be damp, especially for just doing samples. You want it dry when painting as dampness in it while using it for a while will start drawing paint up to the ferrule, making it hard to get clean. The easiest way to dry it is to spin it by rolling the handle back and forth quickly between your hands. They also make a spinner you can buy that does the same thing.

One other thing a lot of people forget. You have to clean out the holes. Those bits don't clean out the hole like a normal drill bit in metal or wood. You need to blow or vacuum them out. You're 3" hole can be filled with debris in the bottom inch. This applies no matter which method of fastening you use. You especially want the hole clean if using epoxy.

I don't think a membrane is enough over a vinyl. A membrane is only used over a properly installed substrate and old vinyl flooring is definitely not a proper substrate. 1/4" durock or hardi board are what you should use. Thinset will not bond well to the vinyl and will start cracking as the vinyl expands/contracts with temperature. I've been doing tile a long time I would never go over vinyl with it. Way back in the day before concrete board and membranes, we still wouldn't put tile over vinyl. We would have used a layer of 1/4" luan. Screwing down another layer also insures the subfloor is solid.

You also need to make sure the floor is perfectly flat when using the tile you are using. Due to the length of them, any high spots will cause major headaches at the joints. The bigger the tile, the more perfect the floor needs to be. You can use a large notch trowel for a thicker mortar bed to compensate some.

As for dry laying, it rarely works out and there is really no need for it. You don't start at an edge. You start in the middle. Find the center of the room and break the room into 4 equal squares. Start at the center and work your way to the wall. in a stair step pattern to keep the tiles running square. Figure out how many tiles( the 6" side) it takes to go from the center to the wall. If the cut at the wall is less than half a tile, shift your starting point a half tile over the center line. This will make your cuts at the wall all be over half tiles instead of little slivers.