What are the legal rules regarding recording music from old demo tapes and public domain music to sell?

Here's a list of all public domain songs:

http://www.pdinfo.com/Public-Domain-Music-List.php

Note that while the music might be in public domain, the performing artist(s) still owns the rights to their recording of it. If a group has specifically released all rights to the music, you can use it.

Under US copyright laws, the only songs in the "public domain" are the following:

1. recordings by the US government;

2. recordings for which the copyright has expired;

3. recordings published in the USA between 1972 and 1989 without proper copyright notice or registration.

There is absolutely nothing any copyright owner can do that changes the legal existence of their copyright. They may, however, "permanently donate their rights to the public domain", which is actually only changing the rights of the copyright owners to later attempt to enforce those rights.

Copyright doesn't require registration to be effective. Always seek the author's permission in writing or risk severe financial penalty. If you somehow change the work such that it becomes a new original work, that's another matter. In that case, it's a matter of how much you changed it. More is better for your purposes.