I will be staying in hotel near Wulingyuan park entrance gate.

I will have 3 full day and nights at the hotel before moving to Zhangjiajie city area for 2 night.
1. Are the Zhangjiajie park entrance ticket for 4 days include the entrance to Tianmen mountain?
2.How do I spend my time [ 3 days and nights] exploring the park when I am at Wulingyuan?

Thank you