Is my fast considered void if madhy (pre-seminal fluid) was discharged with desire, and then I drank water, thinking that its discharge breaks the fast, and do I have to make up for it or offer expiation?

According to the preponderant opinion, madhiy (pre-seminal fluid) does not invalidate the fast. This is the view of Abu Hanifa and Al-Shafi'i. Even if madhiy were to invalidate the fast, one would still be obliged to refrain from eating and drinking out of respect for the month. If someone intentionally breaks their fast after the emission of madhiy, they are required to make up for that day (qada'). Expiation (kaffarah) is only required for breaking the fast through sexual intercourse and is not obligatory in this case due to the absence of a close interpretation [that would necessitate it].