Hey,
So in regards to the public transportation, it's probably mostly mentioned because of safety issues. It's way too hot in the summer months to ride bikes around here, but nowadays in winter it's fine. The biggest concern is that roads have been built that don't really accommodate for bikes yet, so you're better off to drive/be driven. Sidewalks are fine, but I wouldn't recommend riding on the roads. Having a driver makes things easier, but if you're in a central location you can catch cabs pretty easily. Bus systems here are still being worked out and are not very reliable. There are lots of big chain grocery stores in Doha (Carrefour, MegaMart and Lulu) where you should be able to find most of what you're looking for. As for food prices they are a little higher since so much food is shipped in, but it's not marked up too unreasonably. You can find a lot of food that has been grown around the region for pretty decent prices, but you will probably pay more for really specific items that can't be grown around here.
Hope this helps!