How can the intention behind wearing the niqab be made purely for the sake of Allah, especially if the desire to wear it stems from protecting the face from the sun, and what should the questioner do about her feeling that her action is not for Allah, and should she continue her attempt to wear it despite that?

Scholars differ regarding the obligation for a woman to cover her face, and the fatwa adopted by us is that it is obligatory. Therefore, it is obligatory for you to hasten to obey Allah's command by covering your face from non-mahram men. Strive to achieve sincerity for Allah and seek His pleasure. If you add a permissible intention (such as protecting from sunlight), this does not negate sincerity nor invalidate the deed, although it is more perfect for the intention to be purely for seeking closeness to Allah. Do not hesitate to wear what covers your face, for it is obligatory, and there is no prescribed Istikhara prayer for obligations. Strive for sincerity and to seek the pleasure of your Lord, be patient, and seek help through supplication and turning to Allah.