Welcome to HKEx!
Just to be clear - when you say $6/7000 per month is that US$ (i.e. plenty) or HK$ (i.e. not a lot)?
Living - Getting to Lamma at 3am is a taxi ride to Aberdeen and then a rather nausea-inducing ride in a haggled-for sampan across one of the busiest shipping lanes in the world. That isn't a good option in my book!
Practical - Everything electrical is British standards.
Sport - Mountain biking off road is officially controlled - you need a permit and there are limited numbers of trails where you are even then permitted to ride. Pool is reasonably widespread but you need to get used to international rules rather than British ones. (e.g.
http://www.joesbilliards.com ). Snooker is a little less widespread but still easy enough to find. There are plenty of gyms to choose from, from the Municipal ones (apparently not bad for serious trainers), through the ones associated with general social clubs, to the posey ones like Pure and California.
Music - don't know, sorry
Groan List - nothing much - pretty much everything is available here.
Travel - not too bad if you plan ahead - the problem tends to be availability rather than price.
Japan - no, sorry.
HTH.