Good questions, really.
The Battlefield Archer's "Battlefield Experience" feature is rather ambiguous in its description, making it unclear if it allows for a Ranger to apply the Hunter's Quarry to multiple targets with a single minor action. While it does say "at a time", implying that you merely can have it active on multiple targets, it also uses the word "apply", making it sound like using the minor action (which is what applies the Hunter's Quarry) is when you get to select multiple targets.
As for when you get to apply the damage, I'd say it's once per round to the damage inflicted by a successful attack roll, according to the description of Hunter's Quarry. This means that even Close and Area powers only get to apply the bonus damage to one target as you roll an attack roll for each target.
The "Battlefield Experience" path feature simply gives you more options for what to shoot and still gain the bonus damage.