Are the family members invited by the American green card in the same household registration book as themselves? What are the conditions?

Not necessarily from the household registration book. For American green card holders, the only applicants who can guarantee immigration are spouses and minor children or unmarried children over 2 1 year old.

The US green card application for relatives immigrants only includes:

F2a- Spouses and children of American green card holders;

F2b- unmarried children of American green card holders over 2 1 year old;

Australian and Jane immigrants remind that after becoming American citizens, you can guarantee:

The age of married children is 21;

Brothers and sisters. The "brothers and sisters" mentioned here include half brothers and sisters, half brothers/half brothers and sisters, and adopted brothers and sisters.