Melanie, I was just reading the same article you found as well as a few others. Yep, Nanday parakeet but you already know that. They aren't invasive ----- yet. It's that old, just wait a while, story especially here in Fl. In Hobe Sound, where we used to live, there were flocks of Monk's parakeets & they are breeding & moving north -- originally in Fl. down near Miami way. They sure can be noisy! And they would build nests on the lights on the sports fields --- not a good thing to do.
Yes, that is a red bellied woodpecker. It may not be pecking to bring the bugs out. I've read several things that say they hammer on metal b/c it makes a nice loud noise & that's all the better for announcing their territory. Warning other males to stay away & also to attract a female.