Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?
The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.
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.
What is the ruling when the monthly period when exceeding (15) days?
The maximum duration of menstruation is 15 days. If it exceeds this, it is considered irregular bleeding (Istihada). In this case, one must perform ghusl (Ritual bath) after menstruation, pray, and make wudu for each prayer after its time begins. She should return to her previous menstrual habit regarding duration and timing. For example, if her period used to be from the 20th to the 27th of each month, this is considered her menstruation period. Anything before or after this is Istihada, during which she only leaves prayer and fasting for the habitual menstrual days, then performs ghusl and resumes praying.
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.