Is it permissible for a woman to leave her house wearing brightly colored clothing?
Brightly colored clothing is of woman's adornments, however; and this shouldn't be revealed save to her husband and Mahrams. And Allah Knows Best.
What is the ruling of Sharia on looking at one`s Mahram women?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
A Mahram man (man impermissible for a woman to marry) is permitted to look at what usually appears from his Mahram women (women impermissible for a man to marry) while doing their daily housework, with the exception of their private parts. And Allah The Almighty Knows Best.
Is it permissible for a Muslim to slaughter an Aqeeqah on behalf of someone else, and offer it to him as a gift?
In principle, the guardian is the one who should offer the Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) because he is obliged to provide for the newborn, and it is impermissible for anyone else to slaughter it on his behalf unless with his consent. However, it is permissible for a person to offer the sheep, or its price as a gift to the guardian of the newborn, and then the latter can slaughter it, or deputies someone else to do that on his behalf.
What is the best manner in distributing the meat of the Aqeeqah?
It is better to divide all of it as cooked meat amongst the poor and the needy. Dividing it into three portions is a Sunnah, but it is permissible to keep all of it provided that a portion, even a small one, is given to the poor and needy (one kilo for example).