Was what came out of me after waking up from sleep madhy (prostatic fluid), or maniy (sperm), or just moisture? And what is the ruling concerning my prayers if I performed wudu based on the assumption that it was madhy? And is it permissible to wash the area with the intention of it being madhy after performing istinja if I had urinated before it?

You must perform ghusl (ritual bath) if you are certain that what exited you is mani (seminal fluid), and wudu' (ablution) and purify what soiled the body and sprinkle water on the garment if it was madhi (pre-seminal fluid). If you are unsure between the two, then it is more cautious to apply the rulings of both together (purification, ghusl, and wudu'), or to choose between them, which is the opinion of many scholars. Removing impurity does not require an intention or specifying its type. Wudu' is not obligatory immediately after madhi exits, but rather when one intends to pray. Prayers must be repeated if they were performed after madhi exited without wudu'.