Is it permissible for a woman in her menstrual period to recite from the Mus-haf (copy of the Quran ), or to recite by heart?

A menstruating woman is permitted neither to recite nor to touch the Quran according to what Ali Bin Abi Talib (May Allah be pleased with him) reported about the Prophet (PBUH) who was only held from reciting the Holy Quran by Janabah (Major impurity) [Al-Tirmizi in a sound Hadith]. Although Janabah and menstruation are major impurities, a menstruating woman is permitted to supplicate Allah (Duaa`) and make Zikr (Tasbihat ), even if these involved saying words from the Holy Quran, provided that she does not mean the words for themselves but as a supplication, or Zikr. Moreover, she is rewarded for not reciting the Quran during her menstrual period because she abided by the injunctions of Allah.

I`m a building contractor. I have been building a house for a client, but the construction process stopped for some reason. Unfortunately, currently, prices of materials have multiplied, is it allowed for me to demand an increase in the agreed price?

Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?

Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.

Does Istigfar (Asking Allah for forgiveness) between the first and the second part of Friday prayer`s sermon render the prayer invalid?

Talking during Friday prayer`s sermon is disliked, but there is no harm in offering Istigfar between the two parts of the sermon, and it doesn`t invalidate the prayer as it is actually from Sunnah. And Allah Knows Best.