Only Eru, had the power to create life, so how did Morgoth create:
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Yup, as far as the books go, Morgoth could never really create anything. He could only mock creatures created by Eru. Same as Sauron. He could only copy and corrupt others creatures. Some examples are orcs, which were once elves, but corrupted and twisted to dark purposes; wargs, which are probably evil-ler versions of normal wolves; and trolls, which were copies from ents.
However, the other examples you listed, namely dragons and giants, most likely were already part of the world from the beginning, along with other animals.
I have no idea about werewolves. I don't think I remember hearing of one in the series?
Tolkien is never very specific about the details, but Morgoth created orcs by breeding captured elves and men, and thereby creating corrupted copies. Trolls presumably have some ent in their ancestry, and so on. How he got dragons one can only speculate.