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.
Is it permissible to give lessons to mixed students of the seventh grade?
It is impermissible to give private lessons to mixed students since such an act leads to serious consequences for the students in this grade are teenagers.
What is Aqeeqah?
It is the sheep slaughtered on the seventh day from the child`s birth, and it is a confirmed Sunnah after the Prophet (PBUH).
A young man who works for a conventional bank has proposed to me. Is it forbidden to marry him because he works there?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
Since the Messenger of Allah (PBUH) said: "When someone with whose religion and character you are satisfied asks your daughter in marriage, accede to his request. If you do not do so there will be temptation in the earth and extensive corruption."
Marrying such a person is permissible because he is a Muslim, and Allah may bless him with another job in which no usury/interest is involved. And Allah The Most Exalted Knows Best.