Hi,
We presume both your parents are resident in the UK in relation to your questions. We regret that we cannot confirm an answer to question 1. You will need to review Article 7 of the UK / Hong Kong double taxation agreement, which applies to business profits or seek financial advise.
2010 Hong Kong-UK DTA
UK savings income can be declared in writing, where it is not necessary to submit a self assessment tax return. If your mother need to complete a Self Assessment Tax Return, she would enter the interest in either box 1 or 2 of SA100 (page TR3) depending on whether tax has been deducted from the interest.
Thank you.