Mount Huashan from Taiyuan

Hi! I am planning to visit Huashan in the weekend 2-4 Aug 2019
Friday afternoon D train to Xian and then G train to Huashan, overninght base of mountain.
Satuday morning climb up the mountain and visit different peaks, verninght on the mountain.
Sunday dawn, enjoy sunrise, come down and train back to Xian and Taiyuan

questions:
1- Is there a direct train fm Taiyuan to Huashan?
2- How can I book a place to sleep on the mountain?
3- Any suggestions for my plan? we will be 2 -4 people

Thank you in advance