Is hair extension permissible?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is impermissible for the man and the woman to apply a human`s hair as extension, but using artificial hair is permissible for the married woman after obtaining the approval of her husband so long as non-Mahrams don`t see her. And Allah Knows Best.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
Is it permissible for a woman to use a contraceptive without telling her husband although he wants to have as many children as possible and she can`t care for them?
All perfect praise be to Allah, the Lord of the Worlds, may His Blessings and Peace be upon our Prophet Mohammad and upon all his family and companions.
If the pregnancy is harmful to the woman, it is permissible for her to use a contraceptive; however, this has to be backed by a medical report from a God-fearing doctor. In addition, you had better inform your of what you are doing to avoid dispute. And Allah The Almighty Knows Best.