Can you please check for me any high speed train from Guangzhou south station to Xiamen and how long take to reach Xiamen, how many trip per day. Thank you

I'm afraid there is no high speed rail from Guangzhou to Xiamen, but fast trains K229 and K297 are available every day. Both of them departs from Guangzhou East railway station to Xiamen Gaoqi railway station. The whole journey takes about 13-14 hours.

There are D class high speed trains from Shenzhen to Xiamen approximately every half hour.

There are also frequent high speed trains from GZ to SZ. I am not sure if you can travel on one ticket though or need to buy two separate tickets for the journey.

SZ North is the high speed train station in Shenzhen, so connection should be easy. I have not done this journey personally, so my reply is subject to correction.