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.
https://www.law.cornell.edu/definitions/uscode.php?width=840&height=800&iframe=true&def_id=17-USC-1602536950-364936160&term_occur=1&term_src=title:17:chapter:1:section:101
