Is it permissible to perform the Istikhara prayer concerning a matter which the worshipper believes to be obligatory, such as wearing the niqab, while being convinced of its obligation?

It is not permissible to perform Istikhara concerning wearing the Niqab because it is obligatory. Istikhara is not performed for obligations or prohibitions, but rather for permissible or recommended matters when two options conflict, or for an obligatory or recommended act that allows for choice and whose time frame is expansive. This is based on the statement of Ibn Abi Jamra regarding the meaning of the Hadith: "It is general, but specifically intended, for Istikhara is not performed concerning the performance of obligatory or recommended acts, nor is it performed concerning the abandonment of forbidden or disliked acts."