Is ghusl obligatory for a girl if she feels pleasure accompanied by spasms and shivers in the vaginal area, along with the emission of clear, viscous discharge? And must she make up the previous prayers she performed without ghusl due to ignorance of this ruling?

Ghusl is not obligatory merely due to feeling pleasure without the emission of semen. Rather, it becomes obligatory upon the emission of semen, based on the hadith: "Water is only from water," or by intercourse, even without emission, based on the hadith: "When he sits between her four parts and exerts himself, ghusl becomes obligatory upon him." The intention to obligate ghusl merely for feeling pleasure without emission is incorrect, and the movement of semen without its emission does not necessitate ghusl according to the majority of scholars. The sticky secretions that exit upon thinking about desire are madhiy (pre-ejaculatory fluid), which is impure and necessitates wudu' and cleansing what it touches, not ghusl.