Is the prayer valid and sufficient, or is a make-up necessary if a woman prayed with the assistance of a teacher to determine the Qibla, but the teacher's descriptions caused her hesitation?

The information provided by a disbeliever, a fasiq (open transgressor), an undiscriminating child, or an insane person regarding the direction of the Qibla is not accepted. Rather, it is a condition that the informant must be a Muslim, sane, adult, and trustworthy.

If you cannot find a reliable person to inform you about the direction of the Qibla, then you must make an effort and exercise ijtihad (independent reasoning). If you pray without making an effort, your prayer is not valid and you are required to re-do it.

It is also permissible to use precise modern instruments to determine the direction of the Qibla, as they are considered valid if trusted experts among Muslims rely on them.