Is the sum of 2,000 written by the سؤال’s father in the contract considered a deferred dowry (mahr mu’ajjal), a post-nuptial gift (mu’akhar sadaq), or a debt that must be paid, knowing that an advance sum was given to the سؤال’s uncle as a dowry for his daughter?

The non-specification of the mahr (bridal gift) does not invalidate the marriage, and there is no minimum limit for the mahr. Thus, what you paid your uncle is sufficient if he accepted it as mahr.

As for what the ma'dhun (marriage officiant) wrote: if custom dictates the existence of a deferred mahr and you agreed to it, then it is a deferred mahr owed by you. If no such custom exists and you did not agree to what your father said, then nothing is binding upon you. Your father is not bound by the two thousand unless he committed to them. So, the two thousand are either for the purpose of a formal registration, and the mahr is what was presented earlier—in which case they are not binding—or custom dictates the existence of a deferred mahr, and you agreed to them on that basis—in which case they are binding.