"What date were you born?"
Translation:Ulizaliwa tarehe gani?
Nini is only used on its own. You can't use it with a noun. You can't say
tarehe nini for "what date".
What did you watch? = Ulitazama nini?
What movie did you watch? = Ulitazama filamu gani?
Some old prescriptivists would say that "what date" is incorrect in English too and would insist on "which", but that's just silly. English has moved on.