Now
1) As for you (not your child)- need to live in HK for 7 yrs to get PR status
2) Don't know how your child can be a PR , since both his/her parents are not PR in HK (see Art 24(2)(v) of the HKSAR Basic Law)
The Immigration Dept must have made a mistake by considering the child as a Chinese citizen (unless, possibly, if one of his/her parents is of Chinese ethnicity- you should consult the immigration dept about this).
3) Anyway, the status of the child does not by itself change your status in HK
4) China does NOT recognise dual nationality- meaning if the Child is considered a Chinese citizen (which seems to be the case here)- even if the child holds any other foreign passports- he would only be considered a Chinese citizen in HK, and not be entitled to foreign consular protection while in HK or anywhere else in China.
This does not mean, however, that the child cannot gain foreign passports (this of course depends whether he/she is entitled to one). Nonetheless, the foreign passport would be recognised, for a Chinese citizen, as merely a travel document and not a natinality document. THis means the NATIONALITY stated in the foreign passport would not be recognised, and thus cannot have consular protection from foreign countries while in CHina.