The problem with sites such as this to ask questions about taxes is that pilots are too smart, sometimes way too smart for their own good, several expats have discovered that those silly pencil pushers at the tax office are pretty damn smart as well.....! Ask a tax professional with experience in expat taxes about that, sometimes to get advice from extremely smart people is not a good thing.
Commute: I'll answer your question but I would also recommend that you read this thread, it contains answers that you might not think to ask but that will give you a good picture of the lifestyle at AJX.
We get 10 days off in a row (or however you want to use them) and 2 BDC (Blank commuting days) and 24 days of vacation a year that you can also use at your discretion, many people just use 2 vacation days every month.
That means that every month you can make a stretch of 14 days in a row and you commute within those days...., it is a lottery wether you can commute out on the last day of duty, scheduling tries to finish you early enough the last day but sometimes you won't be able to leave until the next day.