You need the same tests from a typed system in a non-typed. You _don't_ need all the tests from a non-typed system in a typed system.
Writing tests to enforce types just hand-rolls a type system, in my experience.
You do though, because invariably people violate the LSP and just "throw Unimplemented" in the methods required by the interface they can't figure out how to implement. In other words all system are duck typed in reality.
Not sure what typing system you're referring to, but it sounds very half-baked at best. I'm using Rust fwiw.
I cannot access any field or method that does not exist. Even dynamic traits are compile time enforced, but i think we can largely have this discussion around static dispatch.