I don't know the answer to all of these situations, but if the author has
explicitly released the work into the public domain you should be fine
modifying and redistributing it (although they should really use CC0 to avoid
ambiguity), while if the author has omitted a license you should assume it is
under copyright. If the author is unknown, the work may still be copyrighted
but it is unlikely to be enforced. The huge collections of "public domain"
programs you refer to probably contain many works for which copyright law won't
be enforced, but I would not assume that before modifying or redistributing
one. Exceptions are if the work is uncopyrightable or the copyright would have
expired by now. For example, in the United States any work published before
1923 is public domain (unless the copyright has been renewed or the work meets
certain conditions), so a folk song written before 1923 is public domain
whether or not the author is known. Recordings of folk songs are another story,
as the recording is considered a separate work from the composition. (From the
link below it seems like it should be a derivative work of the composition for
the purposes of copyleft, but for some reason this is not the case.) If a folk
song was recorded after 1923 it is autmatically copyrighted like any other
work, *but* if it was published before March 1, 1989 the recording has to have
been released with the copyright notice attached in order for the copyright to
be enforcable. AFAIK that last detail is only the case for recordings.
Bascially, copyright law is a shitshow, especially in the States. Thanks Disney.