They're all correct, but they have slight differences in formality. "Does your father have a time machine?" is the most neutral option I think. "Has your father got a time machine?" is more informal and slightly slangish. It sounds more American to me, but people here do still use it sometimes. "Has your father a time machine?" stands out the most. It sounds very formal and a bit awkward to me, but it's not incorrect. "To have" used to always be an auxiliary verb, but now it's usually only an auxiliary verb when in a perfect tense. I believe this usage is more common in parts of England (from previous discussions on italki), but it's generally considered more formal or poetic nowadays.

1) Does your father have a time machine? (present tense) Yes, that's fine. 2) Has your father got a time machine? (looks like present prefect tense but means the same as Q1?) Yes, exactly. 3) Has your father a time machine? (is it correct grammatically?) It is, but it sounds unnatural to the native speaker ear. We do not usually use this form.