GBRF drive the sleeper and CS provide all guards and crew. My knowledge is from the passenger's perspective so someone else will need to tell you about when and where guards and drivers changeover.
Hosts, allocated one per two coaches, and team leaders are divided into London based and Scottish based groups. London crew work all five destinations, so a London host can find themselves out and back anywhere on the network. Scottish crew (should) only work from and to their own location, so for example Inverness based hosts only cover the Inverness section. But it's not unknown for individuals to be transferred ahead of departure from, say, Inverness to Fort William.
It works on a strict pattern of out and back, so you'll alway get Scottish crew southbound on Sundays, Tuesdays and Thursdays, and the Londoners southbound on Mondays, Wednesdays and Fridays. And vice versa of course. This means that they are all returned home on a Saturday morning, ready to start again on Sunday evening.
They stay in hotels during the day.