Do yellow and thick discharges after returning from school, which are considered ṣufrah (yellowish discharge) and kudrah (brownish discharge), necessitate only ablution? And do clear discharges with a slight yellowish tint after watching a historical series count as madhiy (pre-seminal fluid) and only necessitate ablution, or do they have a different ruling? What is the ruling on yellow discharges seen after waking up from sleep due to involuntary vaginal itching?

To determine whether ghusl (definition) (ritual bath) is obligatory for you or not:

If you are certain that what came out of you is maniy (seminal fluid), then ghusl is obligatory.

If you are certain that it is ordinary yellowish discharge (ṣufra), then it has the ruling of ṣufra as explained in the referenced fatwas, and ghusl is not obligatory for you.

However, if you are in doubt about the discharge, you choose between what you are doubtful about and assign it the ruling of one of them. If you wake up and see something you are unsure whether it is maniy or not, you choose.

But if you are certain of the presence of maniy, ghusl is obligatory for you, even if you do not recall a wet dream, while being careful not to fall into waswasa (obsessive whispering).