Are vaginal discharges that do not stop, accompanied by a tremor lasting no more than a second without pleasure or thought of intercourse, considered lust and necessitate istinja’ (ritual cleansing) for fear that it might be madhiy (pre-seminal fluid)? And do they invalidate the prayer if they occur during it? And is this a whisper from Satan?

Ignore the waswas (whispers of Satan/obsessive thoughts) and pay no attention to them. The discharges that exit without desire and are not accompanied by thought are among the usual vaginal moisture. If you are in doubt about them, then choose and assign them whatever ruling you wish. If the discharge is continuous, then perform wudu' for each prayer after its time has begun, and pray with this wudu' both the obligatory and supererogatory prayers until the time for the prayer expires. A tremor does not invalidate the prayer, so continue with your worship.