All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The scholars differed in opinion in regard to a woman in menses reciting the Quran as you have mentioned in the question. For more benefit, please refer to Fataawa 81639, 85112 and 86805.
The preponderant view in our opinion is the view of the Maaliki School of jurisprudence which is also the view chosen by Ibn Taymiyyah that it is permissible for a woman in menses to recite the Quran but she should not touch it without an obstacle (i.e. a glove and the like).
As regards plucking the hair of the armpit, and shaving the pubic hair, then this has nothing to do with menses. A pubescent person should not stay more than 40 days without shaving the pubic hair, plucking the hair of the armpit and cutting the nails; this ruling applies to a woman whether or not her menses are delayed, and whether or not she is in menses. This matter has nothing to do with menses as we have already mentioned. Rather, a woman should shave her pubic hair, pluck her armpit hair and cut her nails when needed and she should not leave this more than forty days as we have already mentioned.
Allaah Knows best.