Yes, that is the way the rental system works out here in Qatar. Now coming to your queries. If your company decides to terminate your services say after 4 months, you must give your estate agent or the owner of your accommodation a month's advance notice of vacating his premises. To be on the safe side, you should give the notice in writing preferably in Arabic and take their acknowledgement. Before leaving the apartment take back from him all the remaining cheques and cancel them.
Have they asked you for a cheque as "insurance"? Most estate agents do. If they have not, then just keep quiet. That "insurance" money is another story going around In Qatar.