Dubai is in the United Arab Emirates, or the UAE for short. It's the biggest city in the country, and the wealthiest.
No, unfortunately there is isn't in either airport, however some of the electronics stores in the International Airport stock Apple goods.
The weather in Dubai is quite mild during December. You can expect temperatures of 20 - 25 degrees, and sunny weather. In the evenings the temperature can drop a little, so it's worth taking a light jumper if you plan on going out at that time.