No. As long as you have earned an unique villain and can afford the threat cost, you can deploy him. If an unique villain is defeated, he can not be redeployed in the same mission by any means.As an addendum to this, this limit doesn't usually if ever include any Allies granted by mission set-up (so it is possible to have Han and Chewie together in campaign if you have earned one and to choose to bring them on the others side mission).
There is no restriction in the number of them.
The only restriction is with Rebel Allies. After arriving at the entrance, the Rebels can choose to bring up to one ally (which they have earned) with them into a mission. (Unless they have a reward card or other ability which tells you otherwise.)