Is it possible to climb Back Huangshan mountain on Day 1 and front mountain on Day 2?

Yes, it is possible. But usually tourists would climb onto the mountain if hiking from the rear mount and take cable car down from the front mount. Climbing from the rear mount takes 5-6h as I know.

Generally, there is not great influence of the closing of Yuping cable car, because there are other cable routes in operation. But I heard the cable car fee of Yuping will climb in the next year.