How is this action or activity called in English when ornithologist attach special small light metal things to birds' paws (I don't know what those things are called in English) in order to keep track of them and study the birds' behavior (like their preferred habitats, migratory patterns, etc.)
This is called "Bird banding", "Bird ringing" (or just "ringing" when the context makes it obvious that you are talking about birds)
We don't talk about "paws" of birds, but rather their "legs" or "feet". Owls, eagles and hawks have "talons".
Wikipedia has an article on ringing