1. Yes, you are able to play a drow. You will spawn in the Underdark, in the city of Sshamath. Please read up on the lore of the city, as its not your 'average' drow city.
2. SoZ is not currently needed. I would assume that it will be needed at some point down the road but honestly it doesnt appear that it will be needed anytime soon. There are no immediate plans for it (that have been announced).
3. There are quite a few quests on the surface.. not so in the Underdark. This is because the UD is relatively new and the surface has been up for a long while... there are plans to introduce quite a few quests in the UD though, so if that is your thing I am sure you will be ok long-term.
Welcome to the server. Please read all of the rules and some of the lore before hopping in. It will make your time a lot more pleasurable, trust me.