You will find many shops for women - wear both stand alone ones and also at shopping malls. Villlagio is one place where you will come across many shops dealing in women's wear. City Center is another. Qatar has a host of other malls where you can find such shops. You will also find such malls having shops selling groceries. As for discounts, usually many shops announce a Sale at least once a year and you can find items at a good price. I am not much aware of shops selling items online here but you may be able to import items after doing an online purchase.
Qatar has several cinema halls. You will come across many pharmacies also. Some medicines are available off-the-shelf while for others you will need a prescription.