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.
Rust is only really a concern if there is water or very high humidity. Temperature doesn't have anything to do with it. In fact the Northeast gets quite dry during the winter so you should have no problems (assuming the garage does not leak).
Proper care of your tools will help prevent rust. E.g. for hand tools you can give them a quick wipe with tool oil now and then, and remove any surface rust if it appears.
A stainless steel cabinet should be resistant to rust anyway, although different grades of stainless steel are better about that than others.
Best Answer
The screw eyes are not rusting. That's staining from the steel rope which i doubt is galvanized. The rust stains will come off with a little emery paper rub.