A female either teacher or student learning quran or doing hifz can do the following during menses - as 3 to 10days will be impure naturally...
الجواب وبالله التوفيق
From this institution the Shara’i solution of the issues is advised according to the Hanafi School of Thought and without need it’s not advised otherwise and the other Schools of Thought are not considered at the time of advice.
The issue which has been asked about is not a new issue, the Ummat has been facing this issue since the period of Nabuwwat. The ruling advised about it in the Ahadith at that time is respect worthy and practicable to date the same way. After this necessary preamble now the answers to your questions are written in order:
ولا یجوز لہم مس المصحف بالثیاب التی ھم لا بسوھا ۔ عالمگیری کتاب الطہارۃ، فصل رابع
و إذا حاضت المعلمۃ ینبغی لہا أن تعلم الصبیان کلمۃ کلمۃ و تقطع بین الکلمتین
البحر الرائق ۔ کتاب الطہارۃ ۔ باب الحیض
واللہ اعلم بالصواب