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.
What is the ruling on wiping over socks?
It is not permissible to wipe over most common socks today because the conditions for wiping are not met. The concession was reported for wiping over leather socks (khuff) and socks (jowrab) with conditions: They must be thick, not allowing poured water to penetrate, enable one to walk in them, be worn while in a state of purity (from ablution), cover the entire foot up to the ankles (meaning covering the protruding ankle bones), and not be torn. And Allah the Almighty knows best.
What should a person who doubted having missed a pillar of prayer do?
All praise be to Allah, The Lord of The Worlds. The prayer of one who doubts having missed one of its pillars is valid, and nothing is due on him/her since having a doubt after offering the act of worship doesn`t undermine its validity. And Allah Knows Best.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.