Is it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and none provided for particularly by whom are obliged to provide for her. And Allah Knows Best.
What is the wisdom and purpose behind the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Among the wisdoms and purposes of the 'aqīqah are the following:
First: Expressing joy at the blessing of Allah the Almighty, rejoicing in the newborn, and giving thanks to Allah for this gift. Allah the Almighty says (what means): "If you are grateful, I will surely increase you." [Ibrāhīm/7]
Second: Proclaiming and publicising the lineage (nasab) of the child — and the 'aqīqah serves as an appropriate and fitting means to this end.
Third: Gladdening the hearts of family members, relatives, friends, and the poor by gathering them together over a shared meal. And Allah Almighty knows best.
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.
Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.