What is the ruling of Islamic Law on following the actions of the imam in prayer and how this following is achieved?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The follower (ma'mum) is required to follow his imam in the actions of the prayer. This "following" (mutaba'ah) means that the follower performs each action of the prayer after the imam has begun it but before he has finished it. For example, the follower bows (in ruku') after the imam has reached the position of bowing, then rises after the imam has risen. The Prophet, peace and blessings be upon him, said: "The imam is only appointed to be followed, so when he says the takbir, say the takbir; and when he bows, then bow; and when he prostrates, then prostrate" (agreed upon, i.e., reported by both al-Bukhari and Muslim).
It is stated in Mughni al-Muhtaj (1/505): "Among the conditions of valid congregational prayer (iqtida') is following the imam in the actions of the prayer... meaning that following the imam is obligatory in the physical actions of the prayer, not in its verbal utterances... Complete following (kamal al-mutaba'ah) is achieved when the follower's beginning of an action comes after the imam's beginning of that same action, while the follower's beginning of the action precedes the imam's completion of it" — end of quote, with slight paraphrasing.
And Allah, the Exalted, knows best.
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.
Is it valid to perform Tarawih prayer at home?
It is Sunnah for a Muslim to perform Tarawih prayer in congregation at the mosque.
However, if a person sometimes prays it at home in congregation with their family for a valid reason, there is no harm in doing so.
Is it permissible to read from the Mus-haf during Tarawih prayer?
Yes, it is permissible to read from the Mus-haf during Tarawih prayer, provided that excessive movements that invalidate the prayer are avoided.
However, it is preferable for the imam to be a memorizer of the Quran and to recite from memory.