Would the purification be considered valid and the prayer acceptable if the area of madhy (pre-seminal fluid) was sprinkled with water and the penis washed without washing the testicles, given that this was forgotten for the Fajr and Dhuhr prayers, and then remembered and washed after Dhuhr?

If you wiped your penis against a wall three times, then you have performed istijmar and purified yourself. Istijmar for madhiy (pre-seminal fluid) is sufficient according to the preponderant opinion, so it was not necessary for you to repeat istinja'. However, if istijmar was not sufficient, then washing the penis and sprinkling water on the clothes achieves the desired purpose. Washing the testicles from madhiy is recommended, not obligatory. Therefore, your purifications and prayers are valid, and you are not required to repeat them.