Is it obligatory to remove the liquids accumulated on the walls of the vulva before every prayer, knowing that some of them might be madhy (pre-seminal fluid)? And does touching the vulva while cleaning it cause the emission of mani (seminal fluid)?

The obsessive whispers (waswas) have taken a toll on you. What we advise you to do is to disregard these whispers and pay no attention to them, as this is the most effective treatment. It appears that these discharges coming from you are vaginal secretions, which are pure (tahir) according to the most authoritative opinion and do not necessitate istinja' (washing after urination/defecation). Their presence is natural. Merely touching the vulva with your hand does not necessitate the emission of semen (mani) or pre-seminal fluid (madhi); rather, this is a whisper from Satan. If you are certain that the discharge is madhi, then you must purify the area and perform ablution (wudu'). If you are certain that it is mani, then ritual bathing (ghusl) is obligatory. Ghusl or istinja' are not required merely based on doubt. If you doubt whether the discharge is mani, madhi, or vaginal secretions, you may choose and assign it the ruling you wish. In summary: Consider this discharge to be vaginal secretions unless you are absolutely certain that it is mani or madhi.