Is it permissible to give zakat to a woman who has no source of income but possesses gold for adornment, or should she be asked to sell the gold first?

If a woman owns jewelry, this does not preclude her poverty and eligibility for zakat (definition) if she owns nothing else, even if the jewelry reaches the zakat nisab (definition). The Shafi'is and Hanbalis have explicitly stated this, for jewelry that is fitting for her and needed for adornment does not prevent her from being considered poor.