I can't speak for all the above named carriers, but I can say that certain employees do live abroad. I know of others who don't, but who end their tours in Europe or elsewhere and travel around on their time off.
In the case of at least one carrier, the company flies you from your home to the airplane, where ever that is. If you're going to be coming from a more expensive, international location, you'll probably be responsible for the cost of your own travel in excess of what it would have cost to get you to the airplane from a stateside location...but you'd have to negotiate that with the company.
Percentage of time spent stateside? Impossible to guess. Each rotation changes frequently once you arrive at the airplane, and there's no telling where you'll be, and when. Generally the airplane begins moving and doesn't stop, so you could be doing back-and forth trips across the atlantic, or you could be continually going east-bound around the world, or doing hops between europe and certain theaters of operation, etc. On any given day you might plan to be going to Hong Kong yet wind up in Lagos, or plan to go to Liege, and wind up in Honolulu.
