What is the ruling on the prayers of one who doubted a wet dream on the Day of Arafah and did not perform ghusl, then prayed in Muzdalifah and Mina, and is it obligatory to repeat them shortened or in full?

If you suspect the emission of semen but are not certain, then ritual bathing (ghusl) is not obligatory for you; this is because the original state is one of purity, and it is not removed by doubt. Your prayers that you have performed are valid, and your pilgrimage (Hajj) is valid. As for spending the night in Mina, the majority of scholars hold that what is obligatory is to spend most of the night there. If you only spent the night there until midnight, you would have contravened what the majority holds.