What is the ruling regarding my circumambulation (tawaf) and ritual perambulation (sa'i) if I see thick, yellow discharge after the Farewell Tawaf and Sa'i, and I do not know when it appeared or from where? Do I have to repeat the Tawaf and Sa'i?

If you doubt the time of discharge, it should be added to the nearest possible time of its exit. So if it is possible that it came out during the circumambulation (Tawaf) and after it, then its exit is estimated to be after the circumambulation, because if something is likely to occur in one of two times, it is attributed to the latter of them.

Therefore, your circumambulation is valid, and you are not required to repeat it. To clarify the ruling on yellowish discharge, please refer to Fatwa No. 125407 and what it references.