First, let me start by saying I am not a lawyer and for questions of legality you should really talk to a lawyer, however I will attempt to answer this from my personal understanding of how I believe the law applies.
You don't need a copyright for the music, you need rights to use the music. Copyright is held by the creator of copyrighted work. If the music is copyrighted, you must obtain a license to duplicate that work in any form. This includes personal use. If you have purchased an MP3 or CD with the song, you have individual use rights which consists of being able to play it for private listening for you and also covers private playing for other people (for example, if you had some friends over, you could play it on your stereo).
It does not give you rights to use the music in a derivative work and distribute that derivative work. You would probably be ok if you used it on a video that you played within the limits of your rights from the CD (playing the video at home for a limited number of people), but if you are going to play it in a public venue or post it to youtube, you need rights to distribute the song which are not included with the purchase of a CD or standard consumer MP3.
You can look for license or royalty free music online that you could use freely. Looking for music released under something like Creative Commons is a decent way to do this, you can also find pay music that is royalty free but requires an initial purchase. To be perfectly clear, unless the specific licensing terms of the music specify additional rights for non-commercial use, it does not matter if you are using it for commercial purposes or not.
There are also some exceptions to copyright (which are referred to as fair use) however, to the best of my knowledge, none of the situations you described fall under fair use.