Structural steel is magnetic - I know this through personal experience.
"Cast" iron is not magnetic.
"Stainless" steel is a very unspecific term and one gets "magnetic" and "non magnetic" stainless steels. The general test that welders use to determine which welding rods to use on (especially on old "stained" "rusty") steel is to scrape an area clear and put a drop of acid on and see if (hydrogen) bubbles are generated. This seperates "stainless" from "mild." If its stainless they will then use a magnet to further determine which rod to use.
These are "rules of thumb."
"Metallurgy" is a facinating science that only in the last 50 years has become more science and less art. There is still some art to it.
I like your doubting and experimental nature!