Is Fajr (dawn) Sunnah a confirmed one?
All praise be to Allah The Lord of The Worlds Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.
How should the udhiyah be distributed?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is obligatory to give the poor a portion of the meat from a voluntary sacrifice (Udhiyah al-Tatawwu’), which should not be less than approximately half a kilogram of raw meat. Other parts do not suffice for this obligation, such as the liver, tripe, or intestines.
It is Sunnah for the one offering the sacrifice to divide it into thirds: one-third for himself and his household to eat, one-third to be given as charity to the poor, and one-third to be given as a gift to friends and neighbors, even if they are wealthy. 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.
What is the ruling of Islamic Law on someone who wakes up in a state of janābah (major ritual impurity) near the very end of the prayer's designated time, during cold weather — should he heat water in order to perform ghusl, even though the prayer's time will expire as a result, or should he perform tayammum instead?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If the water is cold, and cannot be used due to fear of harm that is not ordinarily tolerable, or that would result in illness, then in this case it becomes obligatory to heat the water — even if heating it causes the time for Fajr to expire — and no sin is incurred in doing so, due to his valid excuse. He may not resort to tayammum (dry ablution) instead, since water remains available [and merely needs to be heated].
Imam Shihāb ad-Dīn Aḥmad ar-Ramlī (raḥimahullāh) said: "He was asked regarding a person who, if he were to use cold water, would experience harm that permits tayammum, and who has access to something with which he could heat the water — but if he heats it, the prayer's time will expire. Is it obligatory for him to heat it even if the time expires, or should he pray with tayammum within the prescribed time? He answered that it is obligatory for him to heat the water, even if the time for that particular obligatory prayer expires." [Fatāwā ar-Ramlī, Vol.1/P.98]
Imam al-Bājūrī (raḥimahullāh) said in his Ḥāshiyah on Sharḥ Ibn Qāsim (Vol.1/P.173): "And if he fears [harm] from using cold water, and is currently unable to heat it, but knows of a place where firewood is available, such that if he were to go there he would not return until after the prescribed time has expired — what appears [to be the correct position] is that it is obligatory for him to go and seek the firewood, even if the time expires as a result, as this is the position ultimately settled upon by ar-Ramlī, and as related from him by Ibn Qāsim." And Allah, the Exalted, knows best.