What is the ruling on fasting the two days during which pink discharge and yellowish discharge appeared without certainty of menstruation, followed by complete dryness and the intention to fast despite doubt, and then the onset of explicit menstruation three days later? And does the lack of firm intention on the second day of fasting invalidate the fast?

The pink discharge you saw is menstruation because it occurred at a time when menstruation is possible. Therefore, you must make up for the fast of that day. As for the second day, when you did not see anything, your fast on that day is valid because it is a fast during an intervening period of purity, which is a valid purity. Doubt about whether menstruation will occur does not affect the validity of the fast, as long as you made a firm intention before Fajr.