You'd need two Slingboxes to stream to two different locations (even in the same house). Additionally, you'd need each Slingbox attached to a different Sky box if you want to watch different programs on each TV in Qatar. However you wouldn't be able to use a Slingcatcher. You'd need a computer/Apple TV/Roku/Chromecast attached to each TV in Qatar.
Any current Slingbox (350/500/M1) should provide an acceptable picture.
One concern is that the Slingbox speeds (both upstream and downstream) aren't guaranteed any quality of service--meaning if you start one stream and it takes (say) 75% of your upstream bandwidth in the UK the second stream might only have 25% of the upstream bandwidth to use, resulting in a poorer picture for the second stream.