Which takes precedence: the 'aqīqah or the uḍḥiyyah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is an act of worship through which a servant draws closer to Allah the Almighty in gratitude for the blessing of a newborn child. It is a confirmed Sunnah for those who are financially capable, and Allah does not burden any soul beyond what it can bear.
However, the uḍḥiyyah takes precedence, as it is a confirmed Sunnah established from the Prophet ﷺ through stronger and more numerous narrations — indeed, the Ḥanafī scholars hold it to be obligatory. Furthermore, its time is narrow and limited, expiring with the passing of the days of Eid, whereas the 'aqīqah may be delayed until one becomes financially capable of performing it.
And Allah Almighty knows best.
What fulfills the requirement of Suhoor?
Suhoor is fulfilled by eating even a single date or drinking a sip of water, anytime after midnight and before Fajr, with the intention of strengthening oneself for fasting.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
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.