The various options that long haul pilots enjoy in KE are only available once you join the airline and have completed all the required training and checking. So a minimum of 6 - 9 months after joining.
1) Standard option is to combine annual leave and block time at a location of your choosing. Could be london . Could be Hawaii . You can make monthly selections but most just commute home.
2) Basing. Never mentioned at interviews or advertised. A pilot can select a base. They will report and operate to and from this nominated base ( not position) and as such will be responsible for their own fiscal circumstances. You must be rated and flying the type that serves your base. London was 747-400 but now moving over to 777.
3) Unpaid days off attached to your standard blocks off. Effectivly 2 weeks on 2 off , but for less salary than the standard deal
Double taxation does not mean zero uk tax. If you are resident in the uk you are obliged to make a tax return. Usually the tax paid in the overseas location will be deducted form the uk liability and the difference will be your tax liability. Hence you are not taxed twice on the same salary.As korean tax paid by the airline is no more than a few hundred $US, then good luck with this !
The failure rate at interview is high. 80% fail initial interviews. Off those that pass, around 8 out of 10 will fail some form of the training. Usually the line flying on check. Its by the korean aviation checker. Not the airline. At lease the yanks are in the sim for Boeings.