What is the ruling on advertising an educational channel on channels that contain music or images of unveiled women, or that take posts without the knowledge of their owners? And what is the ruling on purchasing such channels and transforming their content into something purposeful?

There is no objection to advertising your channel on the types of channels mentioned, as long as your channel is permissible and free from শরীয়াহ (Islamic law) prohibitions.

There is also no objection to purchasing any of these channels to transform them into purposeful educational channels, as long as you remove any শরীয়াহ prohibitions found therein.