I'll try to answer you as better as I can (english is not my main language and there are things that I don't know how to explain =S)
1) I think the beak is good as it is, better if you round it, as you say, but I don't see how can you attach it better
2) I've bough sometimes some fiber filling that is compressed, like a sheet (a 2cm thick sheet, but a sheet XD) You could use this, cut the form with the pattern of the tail and put it inside the fabric tail. And sew the end of the body-begining of the tail so that the body filling don't go into the tail. (Same for the fins)
Oh, also, you need to make your fin pattern wider not larger. When you draw a pattern you should take into account that you will stuff it, so it will be a little less wide than you have drawn (I don't know if I'm explaining it right >_<)
3)What I would do is to sew the fins separately (with the filling I've said) and sew the to the body, this way you won't get many rips and the fins will be separated form the filling of the body (so they won't get wonky) If you want to sew all together (body and fins) and flip all inside out at the same time, you have to make some cuts in the fabric before you flip it. Here is some crappy draw (sorry, I only have paint in this pc) where I point where to cut
Watch out you don't cut any stitch, but try to cut very close to it. If you cut it that way, it will get a better shape.
Ok, I hope I've made some sense and this help you with your plushie, tell me if you don't understand anything and I will try to explain it better