Are the fast and prayers of one who saw a trace upon waking but was not certain of its source valid, and must he repeat the fast or prayer if there is no external certainty?

Wet dreams do not affect the validity of the fast. The questioner's fast is valid, and there is no need for her to make up for it. As long as she is unsure whether what came out is maniyy (seminal fluid) or something else, she has the choice [to consider it pure]. As for the prayers, as long as she is not certain of their invalidity, she does not need to repeat them. It is permissible for someone with waswasa (obsessive doubts) to adopt the easier opinion.