What is the ruling regarding the prayer of one who, after waking up, doubts the emission of seminal fluid [ihtilam] and did not perform ghusl, and is not certain whether anything was discharged or not?

You are not required to perform ghusl as long as you are not certain about the emission of semen. Ghusl is not obligatory due to doubt, and the default is the exoneration of responsibility until certainty of its obligation is attained. As for the clothes and places where you sat, they are pure, and there is nothing upon you concerning them.