What is the ruling on the liquid that is discharged after every prayer, and is it considered mathy (pre-seminal fluid) or a natural discharge? And if it is mathy, is it considered سلس ( سلس البول - urinary incontinence/ سلس المذي - continuous discharge of mathy)? And how can one purify oneself from it while preserving virginity? And what is the effect of rubbing on this condition?

You are afflicted with waswasa (obsessive whispering), and the cure for waswasa is to ignore it and not pay any attention to it. Do not search for madhi (pre-seminal fluid). If you doubt its emission, disregard the doubt and build upon the original principle, which is its non-emission. Ibn Baz said: "As long as you have even a slight doubt… do not pay attention to this matter, and attribute it to delusion." If you are certain of the emission of madhi, purify it by pouring water on the defiled area and sprinkling water on any affected clothing. Vaginal discharge is pure but nullifies ablution. The summary is to disregard these whisperings, perform ablution, and pray without caring about the doubts.