
Oterisk |

Druids don't normally get access to Form of the Dragon spells, but since dragon's are capable of casting spells, there is no reason why you couldn't be in the form of a dragon and cast them. If you were in some other form that did not have the ability to cast spells on its own, like an animal, you would need a feat called Natural Spell to be able to cast spells when you were shapechanged.

Tels |

No, it wouldn't. First of all, I'm not sure Druids actual can have access to those spells as it's an arcane spell, and dragons aren't natural creatures.
Second of all, the Form of the Dragon spells do not change you into an actual dragon. You gain only the abilities listed under the spell, you do not gain the spells, or other abilities of the dragon you superficially appear like.
So, if, for some reason, your druid could change into a dragon via the Form of the Dragon spells, then you would only gain the abilities listed (of which spells are not one of). Even taking Natural Spell would not allow you to cast spells, as Natural Spell only allows you to cast spells if you are using wild shape.
You can complete the verbal and somatic components of spells while using wild shape. You substitute various noises and gestures for the normal verbal and somatic components of a spell.
You can also use any material components or focuses you possess, even if such items are melded within your current form. This feat does not permit the use of magic items while you are in a form that could not ordinarily use them, and you do not gain the ability to speak while using wild shape.
However, if you were a Sorcerer using Form of the Dragon, you could still cast spells as Dragons can cast spells. You use your talons to form the somatic movements, and since Dragons can speak, you can speak. Wizards would be unable to cast spells, unless they take eschew materials. Druids, if they could use the spells, could cast spells if they have eschew materials. But, you still need to supply the material component if it costs more than 1 gp. Since your spell component pouch is melded with your form, you can't access it for the more costly components.