Is it permissible to include others in the reward of one`s sacrifice?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible for the one offering a sacrifice (al-muḍaḥḥī) to include another person in the reward of the sacrifice, but it is not permissible for them to share in the price of the sacrifice. It is stated in Mughnī al-Muḥtāj (Vol.6/P.137) by al-Khaṭīb al-Shirbīnī: "If he includes another in the reward of his sacrifice and slaughters it on his own behalf, it is permissible." And Allah Almighty knows best.
What is the ruling on bypassing a nearby mosque for a distant one?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If a distant mosque has a larger congregation (Jama‘ah) while the congregation in the nearby mosque is smaller, and the congregation in the nearby mosque is not adversely affected by the worshiper's absence, then it is better for him to pray in the distant mosque with the larger congregation. However, if the congregation in the nearby mosque would be affected by his absence—such as if he is its Imam, or if his presence encourages others to attend—then praying in the nearby mosque is better. This ensures that the congregation is established in two different locations within the community. This is based on the saying of the Prophet ﷺ: 'A man's prayer offered with another man is purer than his prayer which he offers alone, and his prayer with two men is purer than his prayer with one and if they are more (in number), it is more beloved to Allah, the Mighty the Majestic' (Narrated by Ahmad, Abu Dawood, and An-Nasa'i). And Allah the Exalted knows best.
Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
Can an Udhiyah be made up if its time is missed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the sacrificial animal (udhiyah) is a voluntary (nafl) offering and its prescribed time is missed after the three days of Tashriq have ended, then it is not to be made up as a sacrifice; rather, it becomes merely a sheep for meat.
However, if it was a vowed (nadhr) sacrifice and its time is missed, then it must still be slaughtered, and the slaughtered animal is to be treated as it would have been during its prescribed lawful time. And Allah Almighty knows best.