Zhu Zhou - Causeway Bay(HK). How long and how much by train and which stations to use.

No direct train can take you there. I suggest you go to Zhuzhou West Railway Station to take a high speed train to Guangzhou South Railway Station. The you can go to Guangzhou East Train Station to take a direct train to Hong Kong. The whole journey takes about 4-5h and the ticket fare will be about CNY550-600.
Upon arrival at Hk, you can go to Tsim Sha Tsui to take Tsuen Wan Line to Admiralty Station and then transfer to Island Line to Causeway Bay.