Is another zakat al-fitr obligatory for someone who made up missed days of Ramadan after giving zakat before the Eid prayer? And is zakat al-fitr postponed for someone who was ill and did not fast Ramadan until they make it up?

Zakat (definition) al-Fitr is tied to the time before the Eid prayer, and its obligation is not contingent on the Mukallaf (accountable person) having fasted. The Prophet, peace and blessings be upon him, obligated it on every free person and slave, male and female, young and old, among the Muslims. A Muslim is obligated to pay one Zakat al-Fitr. Whoever pays it on time while not fasting is not required to pay it again after making up the fast. A person who is not fasting must pay it on time, and it is not permissible to delay it.