Is ghusl obligatory for a woman if she reaches orgasm, and what is the ruling on the prayers she performed before knowing this? Does touching the genitals without penetration necessitate ghusl?

Reaching orgasm does not necessitate Ghusl; rather, it is the emission of semen. If semen is emitted, Ghusl becomes obligatory. If pre-seminal fluid (madhy) is emitted, Wudu' becomes obligatory. If nothing is emitted, then nothing is required of her. As for touching the private parts, it does not necessitate Ghusl. What necessitates it is the penetration of the vagina into the vagina, even if there is no ejaculation. Nevertheless, touching the wife's private parts, or vice versa, nullifies Wudu' according to many scholars, whereas our preponderant view is that touching a woman does not nullify Wudu' unless something—either madhy or semen—is discharged. However, touching the private parts without a barrier does nullify Wudu'.