What is the ruling on the trace I find after waking up from sleep, and I do not know whether it is semen or madhy (pre-seminal fluid)? And is ghusl (ritual bathing) obligatory because of it? And what is your advice to Muslim expatriates regarding matters of prayer, ritual purity, and shaking hands with non-mahram women?

If one wakes up and finds wetness, then if they are certain it is mani (seminal fluid), ghusl (definition) (ritual bath) is obligatory. If they are certain it is madhi (pre-seminal fluid), ghusl is not required; rather, they should wash what it touched and sprinkle water on their garment. If its nature is uncertain, then if its cause was something that incites desire, it has the ruling of madhi. If there was no such cause, then they must perform ghusl, wash what touched their garment, and perform wudu (ablution) in order, out of caution.