- Should the fingers be curved/bent or straight?
- Should I press the key actively or let my finger fall by "using gravity"?
Your fingers should be curved, approximately as much as they curve naturally when you hold you hand loosely. Flautists can have trouble with this at first ;). Your hand should be parallel to the keyboard or tilted forward a little.
You'll need to actively press the keys, as well. Even when playing softly you want exact control of how the key is struck. You can use gravity to help when playing fortissimo, though, and having your hand "fall" can be used for visual effect when playing staccato (though many overdo it).
For more on hand/arm position, see my answer here.