Yes and yes.
Use a small synthetic brush to apply concealer. You'll have more control over placement and less of the product will be wasted (i.e., absorbed or left on your fingers). You can use a brush like any of the following, listed in order of preference for the undereye area:
, available at any craft store. You might not like that the brush can leave streaks. I have no problem with that because you can blend away the streaks easily enough either with the brush or your fingers. For 10 bucks, I can deal with that.
Kevyn Aucoin concealer brush
Smashbox concealer brush