Is prayer mandatory on a dying person who goes through a state of unconsciousness, then wakes up?
If he wakes up and was conscious, then he should pray the way/manner he could, but if he wasn't, then he is exempted from obligatory prayer as Allah Says in this regard (What means): "On no soul doth God Place a burden greater than it can bear." [Al-Baqarah/286].
Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?
It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.
What is the expiation for using perfumed soap while being in a state of Ihram(ritual consecration) for Umrah(after making the intent for Ihram)?
It is impermissible to use perfumed soap while being in a state of Ihram, and one who does so is obliged to fast, give Sadaqa(charity), or offer a sacrifice in expiation: He/she either fast for three days, feed six needy persons from the Haram area(one kilo of rice for each), or sacrifice an animal within the boundaries of that area and divide it amongst the poor and needy there. However, it is permissible for him/her to offer fasting after going home.
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.