If I take a private taxi to Hanging monastery, how much will it cost? and half day is enough or not?

Do you mean taking a taxi from DT downtown area to the temple? If so, the fare is about CNY300 – 350 for a single journey. The travel time is about 1.5 hours.
If you just visit the temple and hire a car going and return, half a day is enough. For one hour is enough for the temple.