Hi, short answer to your questions:
1) Presumably you were born in the UK
2) For you to automatically qualify as a Permanent resident in HK (or have the right to live and work in HK without being deported- same concept as Right of Abode in the UK)- when you were born, YOU SHOULD HAVE BEEN A CHINESE CITIZEN. Whether you automatically qualify to be a PR in HK depends on your nationality.
3) Now, only your mother was a HK Chinese citizen wehn you were born. Assuming that one of your parents was settled in the UK or was a UK citizen AT THE TIME OF YOUR BIRTH, and YOU BECAME A UK CITIZEN (British citizen) AT THE TIME OF YOUR BIRTH--> you would be considered under Chinese nationality law to be British and NOT CHINESE.
(Refer to the Nationality Law of the People's Republic Of China)
4) Consequently, you do not qualify for Chinese citizenship by virtue of your mother's Chinese nationality. Thus you do not have the right of abode in HK now.
5) However, you may like to apply for residence in HK. After living in HK for 7 years continuously, you may qualify to be a PR in Hongkong (with British nationality). If you wish, you may also apply for Chinese citizenship (through the HK Immigration Dept), but you'd have to give up your UK citizenship or any other foreign citizenships you hold.