The second Nana Ogawa didn't mean to push Lv Zhi to Liu Bang. He didn't like Lv Zhi, and Liu asked Nana Ogawa to help him and Lv Zhi. Nana Ogawa is just a logical conclusion.
The third Nana Ogawa didn't help Liu Bang and Xiang Yu. Gao Yao wanted to kill Liu Bang when he just became Zhao Gao. Didn't Nana Ogawa tip off Liu Bang? When Xiang Yu arrived in Wujiang River, didn't Nana Ogawa also persuade Xiang Yu to gather across the river? It's just that Nana Ogawa's help is only in some trivial matters. Nana Ogawa himself doesn't know much about history itself. Moreover, he has no talent to change history, and history cannot be reversed by one person's strength!
Fourthly, I think that Nana Ogawa and Yushu were separated from each other by the Tiangong because they wanted to follow the path of the original film because of the influence of the myth of the film version, and because it involves the longevity medicine, if it hadn't been verified for more than 2,000 years, this medicine wouldn't have been effective, right?
Fifth, Nana Ogawa didn't try to open the gate of the Heavenly Palace. It's also explained in the plot. It took him three years to dig the gate of the Heavenly Palace, but every time he chisels a stone, another stone can't automatically repair the place he opened. Later, Nana Ogawa thought of a sentence said by the people of Beiyanshan: "Once the Tiangong is closed, manpower can't be opened!" In this case, Nana Ogawa didn't continue to cut stones to save Yu Shu.
Sixthly, as for why Nana Ogawa moved mountains to save Yu Shu when he had modern equipment, I can only think that it was arranged by the director and screenwriter. Yi Xiaochuan didn't think of this when the writer wrote the plot, and the director didn't want to add such modern elements to the plot when filming, so Yi Xiaochuan was useless, hehe.
All the above are my personal thoughts, for reference only, hehe.