Question on display resolution macbook air 2010
The macbook can output to the apple display at full resolution supported by that display with the extended desktop preference set in system preferences. If you set the mirror desktop preference in system preferences, the resolution will change on the external display to match your macbook. 

I have a dell monitor with display port out and bought a display port to mini display port cable and it works great. There are adapters for basically any conversion, but I suggest a monitor with display port or mini display port because it supports higher resolutions, and it's the future obviously.