All pilots in QR will get the minimum 8 days off per month in Doha, maybe a couple more, of which four will be consecutive. Destinations are Europe, Asia and Africa. Most will be 24 hour layovers so count on 48 hours away from Doha for each trip.
Accomodation will be company provided. You can bid to move to other company accom if you wish. There is a possibility to opt out and get the housing allowance instead, but I think there is a long wait for that. Bringing visitors is not a problem.
Time to start the Command course is around three years after joining. You can expect to do yours on the 787.