Is the one offering the sacrifice liable if its meat spoils?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
If the meat (of the sacrifice) spoils due to the negligence of the one offering the sacrifice in preserving it, or due to improper storage, then he is liable to compensate for the portion due to the poor (which is estimated as half a kilogram of meat). If the sacrifice was a vowed (mandatory) one, then he is liable for all of it.
However, if he was not negligent, then there is no liability upon him, because its ruling is the ruling of a trust (like an item left in someone's care). And Allah Almighty knows best.
A pregnant woman has iron deficiency. When she showers, she becomes very tired and feels cold. What is the ruling on tayammum in this situation?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
One should not resort to tayammum (dry ablution) as a substitute for the obligatory ghusl (ritual bathing) so long as it remains possible to use water — for example, by heating the water, warming the place where the bathing takes place, or taking other similar precautions. However, if such measures prove ineffective, or are simply not possible to carry out, and performing ghusl [with cold water] would result in severe harm, then tayammum becomes permissible in that case, due to genuine inability to use water on account of the harm that would result, as described in the question. That said, she must make up (qaḍā') the prayers she performed using this tayammum.
It is stated in Bushrā al-Karīm: "One should not perform tayammum on account of cold unless warming the limbs fails to remove the aforementioned harm, and no means are available to heat the water — such as a vessel, firewood, or fire — and one fears [that using cold water would result in] any of the harms mentioned earlier in the discussion on illness: danger to life, loss of function in a limb, the onset or worsening of an illness, delayed recovery, or the [visible bodily] blemish mentioned in that discussion on illness. In such a case, tayammum becomes permissible due to the harm involved, but the prayer must still be made up afterward (qaḍā'). If, however, warming the body proves effective, or the means to heat the water are available, or none of the aforementioned harms are feared — then tayammum is not permissible, even if using the water causes some degree of discomfort or pain, since mere discomfort alone does not permit resorting to tayammum." And Allah, the Exalted, knows best.
What is the ruling on someone who is uncertain whether he omitted one of the ab‘āḍ of the prayer, such as being uncertain whether he omitted the first tashahhud?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The ab‘āḍ include the middle tashahhud and the qunūt in Fajr prayer — for which sujūd as-sahw (the prostration of forgetfulness) is prescribed if left out. Whoever is uncertain, during the prayer, whether he omitted one of these elements, should proceed on the assumption that he did not perform it, and should perform sujūd as-sahw accordingly.
It is stated in ‘Umdat as-Sālik (p. 63): "If he is uncertain... whether he omitted a specific ab‘āḍ element, or whether he performed sujūd as-sahw, or whether he prayed three or four rak‘ahs — he proceeds on the assumption that he did not do it, and performs sujūd as-sahw."
The original principle (al-aṣl) for someone uncertain about [having performed] the first tashahhud is that he assumes he did not perform it. And Allah, the Exalted, knows best.
What is the virtue of Laylat al-Qadr?
It is enough to know its great status that Allah revealed an entire surah about it—Surah Al-Qadr. Moreover, the Quran was first revealed on this night.
Allah says {what means}:
"We have indeed revealed this (Message) in the Night of Power: And what will explain to thee what the night of power is? The Night of Power is better than a thousand months. Therein come down the angels and the Spirit by Allah's permission, on every errand: Peace!... This until the rise of morn!" [Al-Qadr/1-5]
The Prophet ﷺ taught us to observe I‘tikaf in the last ten nights of Ramadan, seeking Laylat al-Qadr. Whoever worships Allah and revives this night will receive the reward of worshiping for a thousand months—excluding Laylat al-Qadr itself.