Who should pay the Zakah (obligatory charity) from the orphan`s money?
His/her guardian, and if the latter fails to do so, then the orphan himself/herself is obliged to pay the Zakah once he/she reaches puberty, and is capable of handling his/her own affairs. And Allah Knows Best.
What are the Sharia consequences when the sacrificial time for the uḍḥiyyah comes to an end?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the sun sets on the final day of Tashriq (the 13th of Dhu al-Hijjah) and the Udhiyah (sacrificial animal) has not yet been slaughtered, its designated time has expired. Should a person slaughter it after this point, it will not be counted as an Udhiyah.
However, if the sacrifice was a vowed one (Mandhurah), they are strictly obligated to slaughter it as a makeup act (Qada’), and its meat must be distributed entirely according to the rules governing vowed sacrifices.
It is stated in Bushra al-Karim (p. 702): "If one slaughters after sunset on the final day [of Tashriq]... it does not count as an Udhiyah, unless it was a vowed sacrifice, in which case it is fulfilled as a makeup act (Qada’)." And Allah the Almighty Knows Best.
Is it obligatory to have the intention for each day of fasting, or is one intention sufficient for the whole month?
The intention is obligatory for each day of Ramadan because each day is an independent act of worship separate from the others.
The intention must be made at night before the break of dawn, as the Prophetﷺ said: "Whoever does not intend fasting at night, there is no fast for him." [An-Nasa’i]
And he also said: "Whoever does not firmly resolve to fast before dawn, there is no fast for him." [At-Tirmidhi, Abu Dawood, and An-Nasa’i]
Whoever wakes up and eats Suhoor while mindful of fasting has made the intention. Likewise, one who firmly intends at any moment during the night to fast the next day has also fulfilled the intention.
What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.