Is it considered theft to take Arabic cooking videos from YouTube, translate them, and publish them in Persian on a private channel? And what if the content owner does not respond after being asked for permission?

Intellectual property rights are protected for their owners, and it is not permissible to infringe upon them. Therefore, it is not permissible to publish or translate video clips except after seeking permission from their owner, unless the owner explicitly states that their rights are not reserved.