oooo i like her already cant wait for her to come to Qatar :p So to answer your questions and as they have already been answered
1. Yes you can have sex with your boyfriend, just make sure its YOUR boyfriend and not someone else's, other husbands are also off limits.
2. No you cant live with anyone of the opposite sex under the same roof. Its illegal but still its been going on as long as u have good neighbours who keep their nose out of your business you should be fine but i wouldnt recommend it.
3. Public Display of Affection, depends you can hold hands at the mall, greet by kissing on the cheeks any thing thats innocent and nothing vulgar. You cannot however be caught in a dark area in the back seat of a car making out, you cannot rent a hotel room unless you have a marriage certificate or you are extra smart to know your way around that, do not kiss on the lips in pubic u may hide behind a date tree even if there's no one around but make it quick.

Besides that u can meet a lot of desperate guys at the clubs, they are all the same after a few drinks so take ur pick. If your looking for serious relationship make sure they are not MARRIED first coz seriously a lot of the married men are looking for some nookie every now and then, so follow them home from a safe distance or hire a PI to investigate.

oh and practice safe sex please :)