Does offering Udhiyah (Offering a Sacrificial animal at Aid Al-Adha) avails from offering Aqiqa?
Offering an Udhiyah doesn't avail a person from offering Aqiqa because each of which is a different act of worship. And Allah Knows Best.
Is it permissible to thin the eyebrows or remove them and draw in their place?
Thinning the eyebrows, removing them, and drawing in their place—known as Namas—is prohibited. The Prophet (peace be upon him) cursed those who do it. And Allah Knows Best.
Is it permissible to pay the expiation of an oath to a charitable party as it feeds the poor and needy such as Tkiyet Um Ali?
There is no harm on authorizing someone to handle the expiation of another to the poor and needy, since Shafiee's jurists stated that authorizing someone for the purpose of distributing Zakah, expiation and vow is permissible as stated in [Mughni Al-Muhtajj,vol.3/pp.237]. At last, the intention of the person who intends to authorize someone else suffices in this regard. And Allah Knows Best.
Is photography forbidden, such as photographs of children?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
If there is a need for taking photographs of children or adults, then this is allowed. However, taking photographs of women shouldn`t be tolerated. Rather, they must be taken while wearing Hijab and must be kept in safe hands. And Allah The Almighty Knows Best.