Is it obligatory for a Niqabi woman to wear gloves and socks, or is it permissible for her not to wear them, and would she be sinful if she does not wear them?

Wearing gloves and socks is not obligatory in itself. Rather, it is obligatory to cover the hands and feet according to the Shafi'i and Hanbali schools of thought. If a woman covers them with her abaya or dress, that is sufficient for her, based on the hadith of Umm Salamah that the Prophet, peace and blessings be upon him, permitted women to lengthen the hem of their garment by a cubit to cover their feet.