Is making DVDs and selling them illegal?

Answer 1

No, not at all, provided that you are not making copies of material that is under copyright. If you make and sell recordings of you, performing your own original music for example, that is fine. But copies of anyone else's recorded versions of material is stealing. You are stealing even if you make copies of someone's professional recording of a song when the song is in the public domain. Why? Because it is the song that is in the public domain. The professional performance is itself intellectual property and is owned by someone. A big name artist can record public domain material exclusively. You still can't make and sell or freely distribute that artist's performance without permission. And be careful if you are making an original movie, and you just want background music. There are rights that protect that kind of use (mechanical rights) as well.

Intellectual property is property. Making profit from someone else's property is stealing. If you are making any kind of DVD and selling it, and it contains any material that is owned by someone else, you had better get permission.