Welcome Matthew, Lilly, and flock, thanks for joining!
I watched all of your videos, my first impression of Lilly is she's incredibly sweet and bonded for such short time in your home. As others suggest, that repeated calling is for your attention. Cockatoos demand much time from their people and become insistent. In some cases they become insatiable and resort to self destructive behaviors such as plucking. Your demonstration of wing extension suggests she picks a bit but thus far is not a serious plucker. I would check with her vet before using any supplement, though L-Theanine is considered homeopathic as active ingredient in Avicalm. All you ever want to know about plucking, and hopefully won't ever see:
http://www.parrotforums.com/behavioral/52217-plucking-search-answers.html
Teaching Lilly to self-entertain will be a challenge as you cannot be with her 24/7/365. Lots of toys in her cage and playstand are helpful, especially wood chew items. Parrots are extremely visual and respond to TV, computer monitors, and smartphone screens. Having streaming animal or nature subjects may be a good distraction. Notice you have a Congo Grey and heard other conure-like sounds. Even if Lilly is separated by cage from the others, having them within sight range may be calming. How much time do you spend with her on average?
Please use great caution while walking Lilly outside. Even if you grip her toes firmly, accidents happen and moluccans are good flyers. Many recommend the use of a harness, though teaching her to wear one may be challenging!
Glad you trashed that dollar store seed! A varied mix of fresh vegetables/fruits and pellets or quality seed is best. Let us know if you need suggestions, and our Parrot Food, Recipes, and Diet has lots of helpful threads.
Lilly may benefit from target/clicker training:
http://www.parrotforums.com/training/60435-clicker-target-training.html