Im not sure I can answer all your questions.

BBQ Meat: Generally available at the main Supers (Carrefour etc.) Sorry no pork. The Aussie beef is good.
Drivers License: If you have one from a 1st world country, you just need to do an eye test at the Traffic Dept and they'll transfer it without a road test.
Groceries: Cost is dependant on where you go. But fairly cheap in general. Especially fruits and vegetables.
Alcohol: There's a distribution store (QDC) for alcohol to buy and take home. You need a pass to get in (get it from your HR Department). You get a monthly allowance that is a fraction of your monthly salary. Other than that, alcohol can only be obtained in hotels (at the club, disco, restaurant). Alcohol at QDC is about 1/4 the price of the commerical price in hotels. QDC approx pricing (Crown Royal: 270/QAR, 24 Bud: 130/QAR)
Friends: That's a toughie. After 2 yrs here im still having difficulty with 'friends'. Those are different than aquaintances. Everyone here is friendly though. Some bars are better than others for that sort of thing. But private house parties are where the party is at (im no expert).
Cell Phone: Used and working from as low as 250/QAR. Spankin new with all the options can go for up to 3000/QAR. Call rates are cheap. Average monthly bill should not exceed 500/QAR.
Laptop: Pricey but we've all got one. Maybe your work will give you one. Avg price is 5500/QAR
Internet: ADSL is fast, reliable, and cheap. But only good for one PC. So if you want wireless at home, you're looking at 800-1000/QAR for wireless_router+modem (2 in 1)

Hope that sheds some light.