What does a good Conquest map look like in your opinion?

A good Conquest map caters to the type of map you want to make.  Is it Infantry focused, make it in a tight quarters with lots of objects to hide around and Flags that are closer with little to no vehicles.  Is it more Vehicle focused, make it in a more open area with less objects to obstruct your vehicle movements. On top of that a Conquest map must be open for multiple strategies. The map should evolve and allow for new strategies as players become accustomed to the map. If the map is too streamlined it will quickly become boring as every session played becomes a re-run of the previous session.

What do you think about the potential of introducing Conquest on single player levels?

Single player campaigns for Battlefield Bad Company were built to feel like a multiplayer game, but deliver a compelling story.  Because of that design choice the single player maps just scream for multiplayer goodness. 

Why do you think Conquest has become such a favorite in the Battlefield community? 

Conquest offers an environment for uncertainty, and that is exciting.  Every match is always different without making your surroundings unfamiliar and that leads to unpredictable moments that some have coined Battlefield Moments. It also offers a nice balance to Gold Rush which is objective based and a more controlled progression of your battles.