Im planning to go to the yellow mountain from Beijing next weekend.

you need at least one hour (depends on speed of vel)from tunxi airport to yellow mountain .
There are several route to climb ,and one day is enough for one route.

1. Upon landing, you can take a taxi to get to Tunxi Bus Station first. Then take direct coach to arrive at the scenic area. The whole way takes around 2 hours.
2. The suggested sightseeing time is 2 days.
3. There are several hotels on the top of the mountain. You can go to White Goose Resort. The price is nearly CNY 200 per night. It provides clean environment and kind service. It's located at white goose ridge, north sea scenic area. Hope you like.
4. Yes, from the airport, you can easily find a private car to arrive at mountain area. Don't worry.
But as I know, the opening hours are from 06:00 to 16:30. You have to enter before 16:30.
If not, you can find a guesthouse nearby South Gate of Tangkou Town and tour around the scenic area in the next early morning. You still have enough sightseeing time. About the accommodation, you can stay at Tsingya Hotel. It costs CNY 100 to 150 per night in usual time. The address is Mount Huangshan Tang Kou Zhen Zhai Xi Yun Hui Trade City No. 1-6.