Has Anyone Cheated On Alone

Can anyone tell me where we have to use "has" and where we have to use "have"? I am confused. Can anyone explain me in a simple way?

has anyone cheated on alone 1

I have read a similar question here but that one talks about the usage of has/have with reference to "anyone". Here, I wish to ask a question of the form: Does anyone has/have a black pen? What ...

has anyone cheated on alone 2

auxiliary verbs - Does anyone "has" or "have" - English Language ...

has anyone cheated on alone 3