can we hire a taxi for a day and how much? If no, what about self drive car rental in Xian?

Yes, you can hire, but the fee must be so high. The price depends on where you want, so it is hard to tell you an exact price. In fact, there are many taxi at the gates of every attractive spots. It is no need to hire a taxi.
If you think it convenient, you can rent a car. You can contact eHi, a online car renting company, to ask for more detail information.