Has got используется с 3 лицом (он; она; оно) или то, что можно представить 3 лицом (Екатерина она, Владимир он...)
А have got со 2 (с 1 тоже, но с ним редко задают вопросы)
2 Has Lee got blue eyes?
3 Have you got a stomach ache?
4 Have you got straight hair?
5 Has Sadie got a new computer game?
6 Have you got a favorite thing?
7 Has Jack got a friendly face?
8 Has Mr Hyde got a big nose?