What is the ruling on a quick ghusl without ensuring that water reaches all parts of the body, and without rinsing the mouth and nose? And what is the ruling on fasting when a thin, white, viscous fluid is discharged from the penis after waking up without recalling a wet dream, knowing that a wet dream occurred the previous day without any discharge?

The fluid you saw is madhiy, which is a thin, sticky, white discharge that exits when one feels aroused. It does not necessitate ghusl (ritual bath), but it is impure (najis) and nullifies wudu' (ablution), so it must be purified. Your ghusl was not obligatory as its cause was not present. Your fast is valid and was not broken by water reaching your throat unintentionally, nor by the emission of maniy (semen) during sleep or wakefulness without intentional stimulation.