Is sleeping on the stomach accompanied by sexual fantasies, sometimes followed by the emission of a "thin, clear, white fluid that exits with desire and gushes and removes the desire," considered a permissible outlet for sexual desire, or is it forbidden like masturbation? And what exactly is this fluid?

What exits with desire and gushes forth, followed by relaxation, is semen (mani), which necessitates ghusl (definition). Pre-seminal fluid (madhy) is thinner than semen, and it does not exit with desire, nor does desire cease with its exit. The questioner's statement that Allah made pre-seminal fluid for the discharge of desire in a permissible way is incorrect. Perhaps what he means is a wet dream.