How is certainty regarding purity determined? Are the transparent discharges that appear after wiping considered madhi? What is the ruling on discharges that occur frequently during ovulation? Are the yellowish discharges resulting from inflammation considered impure?

The treatment for obsessive thoughts is to ignore them and pay no attention to them. If you doubt whether the discharge is madhiy (pre-seminal fluid) or from vaginal discharge, you may consider it vaginal discharge, because one who doubts about a discharge may choose between the possibilities.

Normal vaginal discharge invalidates ablution (wudu') but is pure (tahir), whereas yellowish discharge is impure (najis).

If the discharge is continuous throughout the entire time, you should perform ablution after the time for prayer begins and pray the obligatory prayer and as many supererogatory prayers as you wish with that ablution, just like a person with urinary incontinence (sahib al-salas).