The draconic bloodline grants the sorcerer the power to grow claws as a free action, for 3 + CH rounds. These rounds don't need to be consecutive.
If you enchant one or both claws with "magic fang" or "greater magic fang":
1) Does the spell end prematurely, if you choose not to use the claws for one round during its the duration?
Example:
First round: Grow claws, then enchant the claws on the right hand with "magic fang".
Second round: De-grow claws, do something else.
Third round: Grow claws back again. Attack with previously enchanted claw. Is the "magic fang"-spell still active?
There are three explanations I came up with, why or why not the spell could be still active:
The spell has stopped, because the claws do not exist in the second round, so the magic is gone too.
The spell is still active, because if you drop or sheathe an weapon, which was enchanted with the "magic weapon"-spell, it dosen't loose it's magic either. Likewise you could consider your claws "sheathed" inside your fingers.
The spell is still active, because you do not enchant your claws, but your hands. Your claws are part of your hands, if you grow them you just change the type and base-damage of your attacks. See 2) to for more on this.
2) If the spell does not end prematurely, does the bonus "slip" to your unarmed strikes, whenever you are not using your claws?
3) If you keep the enchantments on your claws (for on reason or another), do these enchantments also transfer to other forms, for instance when you are using spells like "form of the dragon", which grants you claw attacks?