will you have time tomorrow. wrong tense but same meaning
I say, "do you have time", for the future. As in, "do you have time in your schedule for tomorrow."
"Will you" is more correct as tomorrow is in the future. "Do you" is more coloquial. They should both be a correct answer.
From Chinese 時間:
Yes although keep in mind that thời is a mutation of thì as in thì giờ.
To have time # to have free time : có thời gian (rảnh rỗi).