Should one who doesn`t perform prayer out of laziness make it up later, and how should he/she do so?
All perfect praise be to Allah,The Lord of The Worlds He/she is obliged to make up missed prayers by offering with each obligatory prayer another one, and if he/she offers two, then it is better. And Allah Knows Best.
How is the niṣāb (minimum threshold) of gold calculated when one owns gold of multiple different karats?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on cash and on gold designated for saving or for trade, provided the total reaches the niṣāb (minimum threshold liable for Zakah), and a full ḥawl (lunar year) has elapsed over it. The niṣāb is (85) grams of 24-karat gold; for 21-karat gold, the niṣāb equals (97) grams; and for 18-karat gold, it equals (113) grams.
If one owns gold of multiple different karats, the person paying zakāh should calculate the monetary value of all the gold he owns, combining these values together to determine whether the total reaches the niṣāb. He then pays zakāh on this combined monetary value, once the total reaches the niṣāb. The relied-upon position is to calculate the zakāh based on the buying price [i.e., the price the gold merchant would pay the owner to purchase the gold from him] on the day the zakāh obligation is due. And Allah, the Exalted, knows best.
Is it permissible to include others in the reward of one`s sacrifice?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for the person offering an Udhiyah (sacrificial offering) to include others in the spiritual reward of the sacrifice. However, it is not permissible for multiple people to jointly share the purchase price of a single sheep or goat, unless one person gifts the money to the other.
It is stated in Mughni al-Muhtaj (6/137) by Al-Khatib al-Shirbini:
"If a person includes someone else in the reward of his sacrifice and slaughters it on his own behalf, it is permissible."
It should be carefully noted that including someone else in the reward of one's sacrifice is completely distinct from offering a sacrifice on behalf of someone else. And Allah the Almighty Knows Best.
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.