An ordinary Japanese learner should probably memorize and as two totally different verbs.
* : to play dumb; to feign ignorance; to play innocent
* : to play stupid (as a joke); to develop dementia
They seem to be etymologically related, but even native speakers do not regard this as a prefix.
Etymologically, according to this article and this question, this seems to be a rare prefix that somehow emphasizes the original verb. Unfortunately I cannot think of another example of in this sense. But / is a common prefix used to emphasize the following word.