No capital S on this one...
Is "Was haben Sie mir" technically correct?
No, "Mir" means "(to) me".
For example: Gib mir das Messer! - Give the knife to me.
Or: Das schmeckt mir gut - That tastes good to me.
Your sentence would be: "What have you to me?" and doesn't make sense.
How to understand when to use "mich" or "mir" ?
After für, it is always the accusative, so "für mich"
Why can't it be Was Sie haben für mir
Mir means to me
Mich is the correct one in this sentence
There are two problems with this construction. (1) The preposition "für" always takes a dative noun, so the correct pronoun is "mich." (2) In the main clause of a sentence the verb is in the second position.