Huawei is the textbook example of how Chinese government own "private". See, for example, http://csis.org/files/publication/130215_competitiveness_Hua...

It is very common to have a "private" company, a party division and government department share a same registration address / contact person in China.

Nobody knows. The ownership structure of Huawei is extremely obfuscated and it has a dual share class system where the employee shares have no voting rights.