It's weird that the rosary Dina's had hidden all this time is all the proof she needs to prove her identity, but she hasn't actually used it yet. Since she has it at all, it will eventually get used for something, but it'll probably be saved for later in the story when she inevitably proves to Teo that she really is the real Dina.
As for why Teo is so sure the real Dina is dead, I'm going to make a crazy guess and say it has something to do with the blue-eyed boy she wanted before she "died". They're alluded to as a 'blue gem' in part 4 and Teo mentions them as someone Dina pointed to and said she wanted right before she died.
Teo's eyes are gray though, so I'm not saying the blue-eyed child was Teo, but he could have some relation to him. That said, this world has the magical ability to not only dye red hair blonde, but also restore the hair's natural pigment with sea water, so anything's possible.
The person who pushes Dina and "kills" her, also calls her a "sinful snake" right before, so they probably weren't someone associated with the Ferlettis. I'm thinking they snuck in. Since the staff was changing so often, who would even know? So, Teo could also have some relation to that person.