rollercoaster,
In a simplistic way you are correct. However it can get awfully complicated if there is no agreement, but then it's your life.
On your second point I think you have answered it yourself. If you are not going to Hong Kong you will be resident in the UK and will have to pay full UK tax. The only way to avoid that is to be resident in Hong Kong and to spend a maximum of 90 days in the UK in any year.