Is it forbidden to use American paid and free software due to the possibility of benefit returning to American companies hostile to Islam? And does the same ruling apply to buying original copies of this software?

The basic principle is the permissibility of dealing with companies. However, if Muslims perceive a legitimate Islamic interest in boycotting the goods of a certain country economically, then it becomes obligatory upon them to do so. As for companies paying taxes to governments, this does not prohibit dealing with them in what is permissible.