@Azuresbend
Okay so I hope I am about explain this well if it confuse's you please let me know. Answering your first and second question on why she is cursed is connected with the Duke. So The Duke hired a witch to curse Flora, the Witch pretends she is a child and acts like she is lost in the castle and Flora being good-hearted person decides to help her.
And the curse part has more to do with beef with Flora's father, King Tarkon. The Duke is King Tarkon's older brother, he originally was suppose to be King when Tarkon and The Duke's father mysteriously died and left a will. The will stated that Tarkon was to be crowned King instead of The Duke (Ardyn is the duke's real name). Their is a whole separate story between Tarkon and The Duke.
Basically The Duke has decided to get back at King Tarkon by targeting Flora who is the Crown Princess and next in line for the throne. I should also mention that King Tarkon has a deep hate for magic (like King Uther from Merlin but toned down a bit) because of The Duke. So the Duke decided instead of killing Flora on spot, cursing her instead, since if there is a magical creature loose near the kingdom Tarkon is likely to send Kinight's to kill it. Especially if Tarkon believe's that the dragon kidnapped or killed Flora.
This leads into your third question about the Knight, the Knight his name is Ayven. He has grown up in Talam and his family is from a long line of Knights and Nobility. So it is expected for any son heir in his family to be a knight, when Ayven would really rather be an Alchemist but follows with the Knighthood to make his sickly Father proud. He is actually pretty close to Flora since the two have grown up together and he is basically a brotherly figure to Flora and her siblings.
The Head Knight convinces King Tarkon to let Ayven help hunt the dragon as a way for him to graduate and achieve full Knighthood. I really like your idea of him gaining Flora's trust then turning on her. (Maybe because he thinks she is lying and actually kidnapped Flora.)
Onto your next question, the Dragons are very intelligent in this world on par and above Human intelligence. They all can speak to Human's and are generally peaceful unless one of their own kind is killed. There also fast to learn while they might not understand some forms of Human Education they are great storyteller's and remember everything. This follows into the Dragon Prince that is cursed to be Human. Ignis, the Dragon Prince is next in line to lead the Dragons so his father made sure he had a good understanding of Humans since he would have to speak and trade with them when he is on the throne.
This also leads into more of how the curse works, the only way the Witch could turn Flora into a dragon is there was an equivalent exchange. This is why Flora and Ignis will have an important relationship since they both are key to the other turning back.
I hope that gives some more insight on the basis of the story and if anything needs more explanation i will be glad to respond.