Can you just say "Çık!" instead of "Dısarıya çık!"?
Would the full form also be correct?
Yes, it is correct. You can also say "Çık dışarı!".
Is leave instead of go our legitimate?
Yep, and it is already accepted.
Can çik be used as going out (dating) with someone?
Wouldn't the translation be "Get out!" in stead of "Go out!"?
They have dıfferent meanings in English, but I think that both can be expressed by çık!
Both correct Turkish answers.