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.
Is Zakah(obligatory charity) due on the money saved for marriage?
Zakah is due on the money saved for marriage if it reached the Nissab(minimum amount liable for Zakah), and a whole lunar year had lapsed over possessing it.
Should I pick up the newspapers thrown at the street because they definitely contain sacred names?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The Messenger of Allah (PBUH) says: "Be mindful of Allah and He will protect you." Part of this is protecting whatever contains the name of Allah. Therefore, if you see a paper containing Allah's name thrown in the street, then you should grab it and similar papers, then burn them in a clean place. Doing so is permissible because Othman (May Allah be pleased with him) has burnt copies of the Quran which didn`t match the main Mus-haf. However, you aren`t required to collect every paper in the street. And Allah The Almighty Knows Best.
Is it permissible for a woman who is in her `Iddah (waiting period) due to the death of her husband to go out and mix with non-Mahrams(Marriageable men)?
A woman in such a situation is only allowed to leave her house for a sound reason such as visiting the doctor, and she is only allowed to mix with her Mahrams(Non-Marriageable kin) since it is permissible for a woman, whether in her `Iddah, or not, to mix with her husband and Mahrams. However, she is allowed to accept condolences, and answer inquiries about her situation after such a calamity.