Oh yeah. You get pairs and, as long as you are patient, nice and thank her after each trade (not only will she not continue, but she won't trade with you anymore if you don't!) you can pick as many pairs as you can during the giveaway time!
Yep. Though, from my experiences, it started off slow, and then got more crowded as time went on because more and more users registered "Oh hey, she's on. I can get Shinies now!" That's when it gets hectic and she needs helpers like me or Yummoon or anyone else on her list to try to maintain order and make sure her rules are enforced.