The bird in the video is definitely a quaker, and now that you know the species you can easily google for information on them to show her pictures. Their alternate name is monk parakeet. They're actually illegal in several states including Pennsylvania because they do pretty well in the wild even in cold places and are perceived as an invasive species. If you get caught with one it will probably be confiscated by the authorities, and if you take it to a vet they're legally supposed to report you. As far as I know this is the only parrot species that's illegal in some places.
http://www.birdchannel.com/bird-news/bi ... aphic.aspxhttp://animals.pawnation.com/guide-owni ... -5120.htmlObviously some people keep them in places where they're illegal, and it's up to you to decide whether you want to do this. The procedure for getting him to come out of the cage is the same as for budgies and other species: gain his trust and give him an incentive/reward for coming out. This involves food treats or some other reward. The cautions about not putting the budgies in a position where the quaker might hurt them still apply.
I haven't checked up on budgies, but with cockatiels the eyes of lutinos usually get darker with age and can look like ordinary dark eyes under normal lighting conditions. There are other mutations that can look like a lutino but actually aren't and have true dark eyes, but the lutino mutation is more common than these. You'll have to ask the breeder to know for sure what he has, but they could be blue lutinos.
The bird in your picture is a lovebird. There are several different lovebird species that are common in captivity plus a ton of mutations. I think the one in your pictures is a black-masked lovebird.
http://www.avianweb.com/maskedlovebirds.html