Can i travel to Terra Cotta Warriors, Mt Huashan and Big Wild Goose Pagoda by Xian metro?

Well, until nowadays, there is no metro that can take you to those scenic areas.
1. To Terra Cotta Warriors and Horse: Take tourist bus line 5 (no.306) from the East Square of Main Railway Station and arrive at there directly.
2. To Huashan Mountain: Take normal trains from Main Railway Station to Huashan Station first. Then take bus 608 to Baoliandeng Square (Huashan Shengtai Square), which is near the entrance of the mountain.
3. To Big Wild Goose Pagoda: Just take a taxi from your hotel.