Is steel impervious?

There are many different types of stainless steel..440c,ATs34, 303, etc..so it heavily depends on what type you're referring to.Ferritic stainless steels would be the ones that have the best...

steel is an alloy made mostly of iron

Yep, you can weld steel to stainless and you can weld stainless to steel. You can use steel or stainless welding rod in either case but the steel or steel welding rod will of course rust.

Stainless steel is steel. Assuming that you mean high carbon steel, and martensitic stainless and proper heat treatment, most of the martensitic steels would be harder with some exceptions.

Yes. It is considered "Mild" Steel due to the low amount of carbon in the steel.