Now- since you were born overseas, whether you fall withint Category iii would depend on whether YOU ARE A CHINESE CITIZEN WHEN BORN.
Article 5 of the Chinese Nationality Law-
(1) Any person born abroad whose parents are both Chinese nationals or one of whose parents is a Chinese national shall have Chinese nationality.
(2) But a person whose-
(i) parents are both Chinese nationals and have both settled abroad,
or (ii) one of whose parents is a Chinese national and has settled abroad,
and who has acquired foreign nationality at birth,
--> shall not have Chinese nationality.
The main hurdle for you may be that you are not a Chinese citizen. Consequently, you do not qualify to be a HK PR.
Concerning the question of "BRITISH NATURALISED"- this is actually a transitional arrangement from pre-1997.
Before 1997, any person who is a Hong KOng "British Dependent Territories Citizen" is a Hongkong PR. If you have this status (which from the information provided, I don't think you do, since your parents did not have this BDTC status)- you would either have ROA or Right To Land in HK (essentially the same, with only slight differences- both entitle you to work, live and study in HK without any restrictions)
Therefore, even if your father is category ii- you don't fit into category iii. The only way through which you may qualify to be a HKPR is by category iv- live in HK for 7 years. (possibly category ii- if you decide to naturalise as a Chinese citizen, but I don't think this helps much in obtaining the PR status in HK)