Is ghusl required and prayers to be redone if a semen-like spot is found on clothing after waking up from a light sleep, with doubt as to whether it is semen and when it exited?

Your prayer is sufficient, and you do not need to repeat it. This is because whoever finds something after waking up and doubts whether it is semen (maniyy) or prostatic fluid (wadiyy) has a choice: if he wishes, he can consider it semen and perform ghusl (ritual bath); if he wishes, he can consider it prostatic fluid and suffice with ablution (wudu') and washing what it has touched.