No bidding for schedules. You are allowed to indicate a preference for two of your days off. They are not additional days off, but two of your 8 minimum days off. Schedules vary, but usually you can expect 11 days off with some rest days mixed in. Also reserve/standby duties are built into your monthly schedule. Usually the standby period will last for a 12 hour period and you have a 1 hour callout to get to the airport. In the last year the most I've had is 3 standbys bulit into my schedule. Lately they have been publishing schedules with something called an available day. That just means 30 hours before the available day the company will assign a flight, standby, or day off. Just looking my Oct schedule I have: 13 flight days, 3 Available days, and 1 standby. I expect atleast one avaiable day will turn into a standby. My days off are in blocks of two except for one block of three days off. The schedules are built to the local FAR max. So if the rules say you need 8 days off, that's what they try to build the schedule with. The rules work a little different out here. Block hours matter less than duty hours when looking at your weekly flying max. 900 hours in a year is the allowed block hours, but the company won't let you fly more than 85 in a month unless you are called from a standby.

This is not a commutable job to the US if that's what you are asking. You can trip trade, but over the last few months it has become very restrictive to where most flights cannot be traded, especially if they are night flights that go into the next calendar day. Occasionally you can find guys who hate long flights to Russia, Ukraine, etc and will swap for shorter days, but usually everyone prefers the longer block days. Everyone except a very small minority avoids the long night flights.

You can leave the UAE at anytime with no restrictions. The longest the company has ever kept my passport was 6 hours to renew my residency visa. The only company permission you need is to purchase a staff travel ticket on Emirates, and that is just a formality to make sure you have the days off you intend to travel. If the ticket is for your wife/kids then it really isn't a factor.