Nice Favilla!
Hey wawa! Sorry it took me so long to respond. I have been away from my computer for over a week since I was at band camp with my son.
Nice Favilla! Lucky you to have scored one. You will never find a uke like it - so don't try! Just treasure that baby, and make lovely music with her.
As far as the case goes, the case you have looks very much like the one I have. Same fake alligator texture on the outside and the same blue lining inside. I do not know if it is an original Favilla case or not. I suspect that it might be since we seem to have the same kind of case. At the time I got mine I also bought a Harmony parlor guitar in an almost identical case - so I thought the case might have been made by Harmony. They also made baritone ukes - but then again, Favilla made guitars. So - I really don't know.
I would think you could take your Favilla on board as carry-on, although I would be careful about putting it in the overhead bins and taking it down. Maybe you could just hold it between your knees. I am very protective of mine, since I know I cannot replace it. I would think it would be worth it to invest in a good case. I have seen some cases for baritone ukes on Musician's Friend. You might call them and give them the dimensions of your uke so they can tell if the case will fit. If it doesn't you can send it back.
Your Favilla is a little different from mine in that you have that white border around the body. Good for you, that is a nice look. The thing I love about mine is the sound. The tone is just gorgeous.
Let me know if you run across good sources for baritone uke music or tabs. I am working on learning classical technique from John King's uke book - but it is strictly for soprano. I wish he would do something similar for baritone. I have also considered buying a classical guitar book - maybe one of Christopher Parkening's books - and trying to adapt it.
Good luck! You have a beautiful instrument. She is worth the effort and attention you spend on her! Happy uking! I hope I will see a video from you and your Favilla!