There are several different words for a “store” or “shop” in Arabic. These include محل (mahall) and دكان (dukaan).
The word محل (mahall) is the most commonly used, especially in places including Egypt. To specify the type of store, you can say:
محل زهور (mahall zuhoor) - flower shop
محل بقالة (mahall baqal) - grocery store; alternatively, one can just say بقال (baqal)
محل ملابس (mahall malahbis) - clothing store
محل كبير (mahall kibeer) - department store (large store)
دكان (dukaan) is used more infrequently in Egypt, though has greater use in other areas (e.g. Kuwait). This word refers to a small shop, such as a neighborhood corner store.
In informal spoken Arabic (colloquial dialects), the word سوبرماركت, borrowed from English, is also used and understood.
Photo credit: stu spivack (Flickr), CC-BY-SA

Here are some words associated with the kitchen (المطيخ - matbakh):

Source: srbyug on Flickr, CC-BY
ثلاجة (thalaja) - refrigerator
فرن (furn) - oven
مغسلة (ma’sala) - sink
أرض (ord) - ground, floor
قدور (quduur) - cooking pots
دولاب (duulaab) - cupboards, kitchen cabinents
نور (noor) - light