Is it permissible for me to supplicate against my ex-wife in prostration and otherwise? And how would that be?

Your relationship with this woman ended with her divorce. If you were wronged, it is better for you to refrain from supplicating against her, for Allah Almighty says: "And whoever is patient and forgives, indeed that is of the matters [requiring] determination." (Quran 42:43) If you were the oppressor, then it is not permissible for you to supplicate, for Allah Almighty says: "Call upon your Lord in humility and privately; indeed, He does not like transgressors." (Quran 7:55) And in the Hadith: "The supplication of a servant continues to be answered as long as he does not supplicate for a sin or cutting off ties of kinship." We advise you to refrain from supplicating in both cases.