Is the wetness I find after waking up, which has no internal or external traces, maniyy (seminal fluid), discharge, or sweat? And does the coldness of the penis area in the underwear, without wetness, indicate the presence of maniyy?

Moisture that has no apparent or hidden trace is not considered to exist. If moisture is found and its nature is unknown (whether it is semen, sweat, or something else), then ghusl (definition) (ritual bath) is not obligatory due to doubt about what necessitates ghusl, for the basic principle is that one's liability is clear until what necessitates ghusl is established with certainty. The mere coldness of the male organ does not indicate the emission of semen and does not necessitate ghusl, and semen has distinguishing signs. It is not necessary to purify the garment or the body as long as the fluid is not deemed impure, for the basic principle is purity. Therefore, the aforementioned moisture has no bearing on invalidating ritual purity or on impurity.