Do we have to purchase in advance train tickets from Hong Kong to Guangzhou, or we can do at site?

Well, of course you can buy the tickets at railway station directly. But in order to make sure you can obtain the tickets, it's still suggested to book them in advance.
TravelChinaGuide provide ticket booking service for you. They are kind and high efficiency. If you want, the contact information is bookingtravelchinaguide.com. :-)