Questions about a Weekend Trip to Xi'an and Mt. Huashan

Hi there,

I am currently planning a weekend trip to Xi'an and Mt. Huashan. Since I live in Shenyang and I have to work during the week, I can be at the Airport at about 10pm on Friday. From Friday to Saturday I want to spend the night at the foot of Mt. Huashan, but I am afraid I will not get to the mountain from the airport at that late time. Exception might be a taxi straight from the aiport to a hotel at the foot of the mountain. Is this possible and how much would it cost me?

Assuming I can get to a hotel at Mt. Huashan on Friday evening, I take the cable car up to the North Peak on Saturday morning and I also take the cable car back down in the evening, will there be enough time on the mountain to do the complete tour (North Peak -> East Peak -> South Peak -> West Peak -> North Peak) including plank walk?

Being back down from the mountain on Saturday evening, will I still get public transportation (bus or train) to Xi'an Downtown?

Thank you very much for your help.

Regards,
Sebastian