What is the ruling on eating or drinking during the second Adhan?
It is not permissible to eat or drink during the second Adhan because it announces the break of dawn and the obligation to start fasting. Allah Almighty says {what means}:"and eat and drink until you can discern the white streak of dawn against the blackness of night." [Al-Baqarah/187].
Whoever eats or drinks during this time invalidates their fast, and they must refrain from eating for the rest of the day and make up for the missed fast later.
What is the ruling on sacrificing a castrated animal or one with a missing tail?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to sacrifice a castrated sheep; as it has been established that the Prophet (peace be upon him) sacrificed:
"...two large, fat, horned, white-and-black, castrated rams (Mawju'ayn—meaning having crushed testicles)." [Narrated by Ibn Majah in his Sunan].
It is not permissible to sacrifice an animal that is missing its tail, or udder due to being cut off. This is in contrast to an animal that was naturally born without a tail, or udder; such an animal is valid for sacrifice. And Allah the Almighty knows best.
What is the ruling on forgetting an integral of the prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Whoever forgets an integral (Rukn) of the prayer and remembers it before reaching the equivalent point in the subsequent unit (Rak'ah), must return to it (i.e., perform it) and complete his prayer, then perform the prostration of forgetfulness (Sujud al-Sahw) at the end of his prayer. However, if he remembers it after reaching the equivalent point in the subsequent unit, the Rak'ah in which the integral was forgotten is invalidated, and the current unit takes its place; he then completes a full Rak'ah to compensate and performs the prostration of forgetfulness.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.1/P.543): 'If he becomes certain at the end of his prayer, or after the Salam—provided the interval is not long according to custom and he has not stepped on an impurity—that he omitted a prostration from the final Rak'ah, he must perform it and repeat the Tashahhud, as his previous Tashahhud occurred before its proper place. If the omission was from a Rak'ah other than the final one, he must perform a full Rak'ah, because the deficient unit was completed by a prostration from the subsequent one, rendering the rest of that subsequent unit void.' And Allah the Exalted knows best.
What are the pillars of fasting?
The pillars of fasting are intention and abstaining from all nullifiers of fasting from dawn to sunset.