Should one repeat the prayer if, immediately after finishing the prayer, remnants of water used for istinja' are found, along with a slight sheen on the tissue that appears to be clear discharge, though it is uncertain whether it is discharge or not? And would repeating the prayer in this case contradict the Prophet's (peace and blessings be upon him) saying, "Do not pray a single prayer twice in one day," especially considering that scholars have stated that prayer is not repeated except for a man in congregation to attain the reward?

We fear that what you mention is merely a whisper (waswasa). If so, then turn away from it, and do not repeat the prayer merely due to doubt. The default is that nothing has exited until there is absolute certainty. If you are certain that something exited from the private parts before or during the prayer, then repeating the prayer is obligatory due to the loss of purity. This repetition is not included in the prohibition against repeating the prayer twice, because the first prayer was invalid. All of this is conditional upon certainty that something exited from inside the private parts before or during the prayer. Without this certainty, the default is that the prayer is valid.