Rome - Guangzhou - ?Hong Kong? - Taiwan

No, this is not possible. You cannot use train to reach Hong Kong by train because taking a train is not eligible under any visa free transit scheme. It is possible to use a ferry, but in that case, the requirement is that you stay first in Guangzhou for at least a minute longer than 24 hours. Also, you have to be aware that you are allowed to return to Guangzhou by flight only in order to continue your journey to Taiwan.

To summarize, this "side trip" to Hong Kong is not possible during such a short time frame and, as you can see, it involves first taking a direct ferry that has to be booked in advance as well as the flight from Hong Kong back to Guangzhou because the flight toward Guangdong province, where Guangzhou is located, is the only eligible way of entry under visa free transit scheme.

Just to conclude, you will have to postpone your trip to Hong Kong and in Guangzhou you will be covered by 144 hour visa free transit and you do not need any kind of visa. Just for your comfort, I assure you that you will find nice attractions and details to fulfill your layover in a very meaningful way even in Guangzhou.