What is the ruling on dealing with files created by unlicensed software, and is it permissible to deal with them if that is confirmed, and is it obligatory to inquire about their source if there is doubt?

The basic principle is that a person's financial liability is clear and sound, and one is not required to investigate the source of what another possesses when dealing with them. The fact that files might have been created using pirated software does not prevent dealing with their owners, because the right of the software owner pertains to the liability of the one who benefited from their copied software, not to the file itself. Therefore, there is no harm in dealing with these files, and you are not obligated to investigate the programs with which they were created.