Donny, those are some very broad questions that involve legalities. Please don't take this advice as being from a legal expert...
No music, commercially available or otherwise, can be used, distributed, etc. without the express permission of the copyright holder. It is generally accepted that individuals who have purchased a legal copy of a song, may copy the song and use it in their home videos, assuming it is for personal use only.
Note that there are rights that are pertinent to the title and rights pertinent to the performance. For that reason, even a title that is in the public domain may not be freely used without the permission of the person who holds the rights to that particular performance.
It is prohibitively expensive for a small-time video producer to acquire the rights to a popular piece of music. There are, by the way, several types of "rights", the description of which would take more space than these posts are intended for.
There are companies who sell rights to music they have performed and either wrote or the titles are in the public domain. You'll find several of those noted (and linked) in these forums, if you use the Search feature.
You can also buy software like Cinematize or Sonicfire, that creates loops and can time them to your video pieces.
There was a recent magazine that had an excellent article on this subject. I can't recall for sure, but I think it was either "Digital Video" or "Event DV".
As for insurance, there is liability insurance, equipment coverage and "errors and omissions" insurance.
You can learn more from places like -
http://www.videouniversity.com
http://www.4evergroup.org
http://www.weva.com