If an independent executive of an estate is paid 6300 dollars does she have to pay taxes on that?

It isn't an inheritance. It is a payment for services rendered. Just like anyone else getting paid for work. (If she actually is a lawyer or accountant, or as administor she hired one, would you have any question if those payments were income to the recepient?) Taxable. I believe the estate she was managing needs to provide a 1099 too.