When applying thinset, put it on in a flat coat first,, and lay it on thick, pressing it against the wall or floor. THEN go back at an angle and notch it, removing excess. This makes sure the thinset has good contact with the wall over the whole area and will bond well. Laying it on at an angle, so it's notched in one pass, doesn't spread the thinset over the wall nor press it into the wall as well as laying it flat first.
Use a V-notch trowel, definitely; A narrow U-notch will work in a pinch, and don't bother with square-notch; those are for laying floor tile mostly, where you need a lot of vertical play to create a level surface. If the mesh tile doesn't seem to be adhering well to the wall, you can try "back-buttering" the mesh with some more thinset, kind of like applying glue to both sides of a wood joint. Just don't damage the mesh or lose too many attached tiles. Don't be afraid to really lean in with pressure to get the tiles into that thinset; just don't pound on the tiles/wall too hard.
OK, a few definitions:
Yield strength is the amount of force required to cause the steel to yield, which means permanently deform (i.e. permanently stretch).
Tensile strength (a.k.a. "ultimate strength") is the amount of force required to cause the steel to actually break. This will be equal to or greater than the yield strength.
Minimum just means that the steel will be at least that strong.
Hardness is a measure of how resistant the steel is to scratching and denting. For structural usage it's probably not important, but would be important if you were looking for a durable finish, e.g. a workbench top or a tool bearing point.
Stiffness (you didn't ask about this, but it's another way of looking at the strength of a material) is a measure of how much something deflects when you put a force on it. Steel alloys tend to be pretty similar in this regard.
As you can see, "strongest" doesn't really have a specific definition, it depends on what you're looking for.
Here's an analogy for the difference between yield and tensile strength:
Imagine you have a spring. You pull on it a little, and when you let go it returns to its original shape. This is "elastic deformation", and no damage has been done. Now you pull hard on the spring and it doesn't return to it's original shape anymore. The material has yielded and you have "plastic deformation". This may or may not be considered "failure", depending on the application. Now pull really hard and the spring breaks. That's the ultimate strength. Clearly the spring has failed now.
As for the ranges: "steel" is a non-specific name for several alloys and it can be made in several grades, hence the ranges you've found. The material is usually designated with an alloy number. "Cold rolled" and "hot rolled" are methods for shaping the steel, and don't really tell you anything about the strength.
I should also point out that all of these properties that I've mentioned are for the steel material itself. If you want to know the behavior of an actual piece of steel, you need to know both its material and it's shape.
Best Answer
Don't bother patching the holes in the drywall.
Backsplashes are usually 304 stainless steel. In the US, you could order that from onlinemetals.com. (No, I don't work for them. I recently replaced my range hood and have the same problem as you.)
You should get a metal shop to cut the metal with a jump shear. It is very unlikely that you can get a nice edge for less money using hand shears or a jigsaw.
I'm not sure about the glue. My old backsplash has some kind of adhesive padding behind it. I'll probably try Liquid Nails LN-203.