Is what the questioner feels—that some words he hears or actions he performs might be disbelief (kufr) or mockery of religion—a real matter or merely whispers (waswās), and what should he do if he feels that way?

Thinking in this way is a form of waswasa (whispers/insinuations from Satan), and you must disregard it and not give in to it, lest you fall into great distress. To understand the nature of mockery (or ridicule) that expels one from the faith, please refer to Fatwa No. 109383. To understand the importance of getting rid of waswasa in this matter, please refer to Fatwa No. 113780.