Catch the bird on top of the notice board?

No, you cannot. The bird is simply there to let you know that there's a new post on the message board that you haven't read yet. This is actually a very common question for every game, and often people will post trolling messages trying to get players to jump through hoops to catch it, but the sad reality is you cannot.

No, there isn't. The bird is just there to notify you that there are new notices on the bulletin board. If there are any unread notices the bird will appear, otherwise you won't see it.