Who do I call about booking high speed trains from Hong Kong to Shenzhen and to other cities?

I’m afraid you cannot go to SZ by train, for there is no train from Hong Kong to Shenzhen. Maybe you can take the MTR to Lo Wu reaching SZ. There are through trains from HK to Beijing, Shanghai, Gunaghzou and Dongguan. I had booked the through train tickets by a travel agency, the website you are visiting. I remember their contact info is bookingtravelchinaguide.com.