Immigrants can be brought back to China.

Hong Kong identity has nothing to do with nationality.

You can go through the relevant formalities in Hong Kong with your Hong Kong identity card and mainland passport.

Because of investment immigration, mainlanders must apply with the right of abode in other countries, while your father applied with the right of abode in other countries, so he did not cancel the mainland household registration. Only when applying for permanent residence in Hong Kong, the mainland requires that the mainland household registration must be cancelled.