Is it permissible to write verses from songs or catchphrases from movies and plays if they are free of impermissible (shar'i) content, knowing that the listener might know their source and watch the film or listen to the song, and does the writer bear the sin for that?

It is permissible to write poetic verses that are free from Sharia prohibitions. However, the source should not be mentioned to avoid tempting others to listen to or watch something forbidden. If the reader knows the source and goes to it, there is no sin upon the writer, Allah willing. It is advisable to avoid writing such verses if there is no benefit in doing so.