Is it permissible for a brother to give Zakat to his orphaned sisters who have no income and live in their father's house under the care of their stepmother who refuses to spend on them? And is Zakat obligatory on gold used for adornment with no intention of selling it, given the absence of income to cover this Zakat?

It is permissible to give zakat (definition) to a brother if the recipient is among those eligible for zakat. Similarly, it is permissible for a brother to give zakat to his sister if she is among those eligible. As for jewelry, zakat is not obligatory on it unless it reaches the nisab (definition) (minimum threshold) or if it is intended for use and adornment.