Hi! Is it possible to go directly from Terracota warriors to Mt Huashan? By bus, train or taxi?

No, there is no direct public transportation and transfer is needed if you wanna avoid getting back to Xian. Well, take a taxi from the museum to Lintong Bus Station, where you can take a bus to Weinan. At this bus station, you can easily take a direct bus to Huashan Mountain. If hirng a taxi or private car from the museum directly to the mountain, it may cost CNY500-800.