Is there a nisaab on zakatul fitr like the yearly zakat or are these two one and the same. If not how do we know who is liable for paying the zakat. And when paying for those under you care, does this apply for a non Muslim under you care?

There is no nisaab when it comes to zakatul fitr. The fitr is upon a Muslim to be paid on his behalf and on behalf of his dependents (Muslims).  One Saa’ of dates or one Saa’ of barley or one Saa' of your country's staple food should be given. One Saa' is equivalent to about 3 kilos and the Prophet (ﷺ) commanded that it be given before the people went out to the (Eid) prayer.