By bead, they mean little plastic beads like you'd see on a homemade necklace. Ranging from pearl size to smaller. They come in various colors and are used as egg imitations. Can buy your flies at Michaels, lol.
People tend to make their glo-bugs too big. Real eggs are small. They also probably sink better than soft materials like glo-bug yarn. IMO that's probably part of their secret.
Yeah, the Alaska rig is having the bead a few inches up the line, then a bare hook trailing. The theory is that the fish bites the bead, then when you set, you pull the hook through it's mouth, either hooking the outside or inside corner of the mouth. You can use bigger hooks with small beads that way, as well as things like circle hooks, and you tend to hook up in the corners of the mouth where there's less danger of him throwing the hook during the fight or rubbing his teeth on the line.
The criticism is that it's a way to snag fish. If fish moves out of the way of the imitation, he may move into the hook. Also, some argue that, even if the fish hit the bead, if the hook enters the outside of the mouth it is foul hooked and therefore unsporting.