The source of Dragons

[NightKnight]

Morgoth couldn't create anything by himself, but he and the other Valar/Valier created ME through song with the unknown guidance of Eru. However, Aule created the dwarves, and Yavanna the two trees. Therefore, would Morgoth not have some power to create a form of life?

After Aulë created the dwarves, Ilúvatar says something about them not being to move unless he was thinking about them. But then he adopted them and gave them own life. The same might go for Morgoth, but I don't think it applies to the dragons, as they were able to move even after he was thrown out of the world. Another example of the move-when-someone-thinks-about-you thing is at the battle of Morannon. When Sauron discovers Frodo, all his thoughts go there and his servants stop moving.
As for Yavanna, I think plants are a bit different from creatures. Plus the fact that growing plants was her specialty.