What you are missing in your strict logical deduction is this detail:
/stato, stata, stati, state/ form the past particle of /essere/, therefore question
is expressed with 'essere'. (How has your breakfast been?).
Moreover /essere/ has itself as auxiliary (while in English it has /to have/), but I'm quite sure you know this already!
The rules about /stare/ versus /essere/ are not a few, and exceptions also exist.
If I get the time I'll write another answer.
Bye!