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.
What is the ruling on mentioning Allah`s name upon slaughtering an animal?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is a Sunnah (prophetic tradition) for the person slaughtering to say: "Bismillah" (In the Name of Allah), though the most complete and perfect phrasing is to say: "Bismillah ar-Rahman ar-Rahim" (In the Name of Allah, the Most Gracious, the Most Merciful). This is in accordance with the words of Allah Almighty: "So eat of that [meat] upon which the name of Allah has been mentioned." (Al-An'am/118)
However, pronouncing it is not an obligatory requirement (Wajib). If someone omits it—whether deliberately or out of forgetfulness—the meat remains entirely lawful (Halal) to eat, though purposely omitting it is considered disliked (Makruh). And Allah the Almighty Knows Best.
How do I deal with whispers (waswasa) in ablution and purification?
Whispers in ablution are from Satan, and the Muslim should not pay attention to them. He is not required to re-perform ablution or repeat washing a limb because of waswasa. He should always base his purification on its being valid. It is recommended for him to frequently say "La ilaha illa Allah" (There is no god but Allah), because Satan recoils when Allah is mentioned. And Allah the Almighty knows best.
Is it permissible for a woman to perform the obligatory prayer immediately after the adhan and before the Iqamah is performed in the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible for a woman to perform the obligatory (Fard) prayer immediately after the Adhan (call to prayer) and before the Iqamah (call to commence prayer) is performed in the mosque. And Allah the Exalted knows best.