Is vomit among the nullifiers of Wudu (ablution)?
Vomit does not nullify Wudu, but it is a Najaasah (impurity) that requires rinsing the mouth and washing whatever became dirty by it since the prayer becomes valid only after the removal of Najaasah. And Allah Knows Best.
How many prostrations of Quranic recital are there, and is it permissible not to offer them while reciting?
There is one prostration for the Quranic recital, and it is a Sunnah for which one is rewarded upon offering it. However, one who doesn`t isn`t punished. Therefore, those who fail to offer it aren`t considered sinful, rather they deprive themselves from the reward.
What should one who made an intention, at night, to make up for a missed fasting day, but broke his fast on the next day?
One who started making up a missed fasting day, then broke his/her fast without a legitimate reason is considered sinful, and is only obliged to make up for the missed fasting days. And Allah Knows Best.
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.