How is Zakat al-Fitr to be given by a Muslim woman temporarily residing in a non-Muslim country? Should it be given in her home country or in the country of her temporary residence?

The basic principle is that Zakat al-Fitr is to be paid to its rightful recipients in the country where it became due. If there are Muslim poor people in the non-Muslim country, it should be given to them. Otherwise, it is to be given out in the country of the one who is paying the zakat.