Yes, great-grandfather was grandfather's father. His great-grandfather was his great-grandfather's father, which was also his grandfather's father.
Han Gaozu's father was Liu Zhijia, also known as Liu Taigong.
No, grandfather is grandfather, and grandfather's father is great-grandfather.
Gaozu's father called him Tianzu. It was mentioned in Erya Shiqin: " Those who gave birth to themselves are their parents, their father is their grandfather, their grandfather's father is their great-grandfather, their great-grandfather's father is their great-grandfather, and their great-grandfather's father is their great-grandfather." Therefore, Gaozu's father was called the Heavenly Ancestor.
Liu Bang's father was called the Heavenly Ancestor.
Liu Bang's father's name was Liu Taigong.
Liu Gaozu's father was called Liu Wei.
Liu Bang's father was called Liu Taigong, and some people called him Liu Wei.
Emperor Gaozu's father was called Liu Taigong.