Is it permissible to pay Zakat to feed a large family gathering (500 people) for a period ranging from three to six days, given the presence of individuals who cannot pay or refuse to do so, and their need for money?

It is not permissible to use Zakat funds to feed gatherings. The uses of Zakat are precisely defined by Islamic law, and they do not include feeding guests or gatherings. If there is someone among them who is eligible for Zakat, the Zakat should be given directly to them, not used to feed them.