3. If a family member's application to immigrate to Hong Kong is rejected, is there any channel through which I can appeal?
If your case involves the refusal of a one-way permit for a resident of Mainland China, then you must approach the relevant Mainland authority, as Hong Kong government officials do not have the legal authority to grant this permit.
If your case is related to a rejection by the Hong Kong Immigration Department of an application by a non-Chinese family member in a foreign country, then you should first contact the Immigration Department to see whether there is any missing or incorrect information that you could rectify (and try to ask for a review of your application).
If you are still unsatisfied with the decision of the Immigration Department, you can consider applying to the High Court for a judicial review. However, you should note that judicial review is not an appeal process, and the grounds on which the High Court can rule in your favour are very restricted. You must seek legal advice before making this application because substantial time and legal costs will be incurred.