Traveling to Xihai (Huangshan Mountain) from Shanghai via bullet train on Sept 9th

Yes, it goes into North Railway Station. You need to go to Huangshan firstly because your hotel is in the scenic area. You can take bus at Coach Station near the North Railway Station. It departs from 9:15 to 20:20 with interval of 30 minutes and costs CNY20 with 50 minutes. You need to take Yungu cable car to the peak of mountain to your hotel.

Very helpful - Thank you!

I know people walk at different pace, but how long would it take to "hike" from the Yungu cable station to Xihai hotel (ballpark)? 1/2, 1, 2 ... hours?

Around 1 hour.

Can we take the Taiping Cable car to Purple Cloud Station instead? That station looks nearer to Xihai Hotel.

I had originally planned on going to the Taiping cable car thinking it would be quicker and easier. However, I'm not sure that it makes a difference time wise. We would be taking the scenic bus from the North Railway station, which goes to the south entrance, and would need to take a taxi from the southern mountain entrance to where the Taiping cable car was located (north entrance). The hiking from Taiping cable car to Xihai hotel would be shorter, but probably close to equivalent time wise when you factor in the taxi ride. If, we were coming from the north side, then we'd use Taiping cable car.
Yungu cable car is a more appealing route for us, since, I'd rather hike on the mountain than take a taxi.