Just needs a "to hit" factor. Does it base off of dex like a talon would? 

The Aasimar uses their DEX as the modifier to hit. 

I like this ability but I have a few questions. Is this a full action? Does it replace a single attack if the character has multi attack? Can they use this ability any time or just while they have their wings/aura up? does each feather need a separate attack roll? I suggest looking at the Magic Missile and Eldritch Blast spells for explanation wording suggestions.

Good question Ozgand, 

I do see them like the magic missile spell,  that it can be  directed toward one opponent or multiple. The player does use use DEX to hit like a range weapon. Takes just one successful "to hit".  Example player rolls d8 for number of feathers. Player rolls a 5. If the player hits an opponent using his DEX modifier,  and the player has a +3 on CHA. Damage would be 1d4+3 X5. 

Casting time: 1 action

Range: 60ft

Can only be used when wings are present.