Since a macro is a definition of syntax, I think you'd essentially need something like typing judgments to show how the typed elements of the syntax relate to one another, so that the type checker (e.g., a typical Hindley-Milner unifier) can use those rules. These are usually written as the fraction-looking things that show up in PLT papers. This is, as GP says, essentially extending the type system, which is a task fraught with peril (people write entire papers about type system extensions and their soundness, confluence, etc.).

Depends on your point of view really. I'd define a macro as a function with slightly weird evaluation rules.

If you want to write a macro where any call to it which typechecks creates code which itself typechecks, you have to deal with eval of sexpr which is roughly a recursive typecheck on partial information, which sounds tractable to me.