How do I go to Hong Kong by MRT, near Guangzhou Hotel, GZ? How much the fare per person?

It is impossible to travel to HK from GZ by MTR.
Two ways are suggested for you. You can go to the local East Railway Station to take the direct trains to reach HK. The fare is around 190HK$ per person.
Or you can find direct trains to reach HK from China Hotel and China Landmark Hotel. The China Landmark Hotel is near the Haizhu Plaza. The fare is different according to different operation companies.

Ho do go to Hong Kong by Bus from GZ Hotel? How much is the fare per person?

Thanks.

From GZ Hotel, you can also find the cross-border bus at 07:10, 07:20, 07:40, 08:40 and 14:00 and the bus fare is around 90HK$ for reaching Kowloon area and the Central area.