Does the younger brother have guardianship over his unmarried elder sister, and is the niqab obligatory?

An elder brother does not have the authority to discipline his sister by virtue of brotherhood, because the authority to discipline belongs to the ruler or his deputy, or to a specific guardian such as the father or grandfather. As for your sister abandoning the niqab, you should advise her and persuade her with wisdom and good admonition about its obligation. However, you do not have the right to force her to wear it, as the niqab is not a matter of consensus among scholars, and "there is no denouncement for matters of disagreement, rather denouncement is for matters of consensus."