looking for a night time schedule and fares for trains from hong kong to taishan then to Xi'an

From HK, there is no train to Taishan.
I helped you to check it and found that there is a train from Guangzhou to Taishan directly. The train takes about 21 hours. The train is T180.
From Taishan, there are 6 trains to Xian.
From HK airport, you can take a direct bus for Guangzhou directly. Then hire a local taxi to the GZ Railway Station.

If you do not want to take such a long time train from Guangzhou, you can fly to Jinan first, but you need fly to Jinan from Shenzhen.