Is wearing a cap permissible for boys, or girls?
All Perfect Praise is due to Allah, The Lord of The Worlds.
In principle, anything is permissible sol long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden. And Allah Knows Best.
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
What is the ruling of Sharia on using IUD (Intrauterine device) temporarily and by mutual agreement of husband and wife?
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.
There is nothing wrong with this if this device is used on temporary basis and by mutual agreement of husband and wife since this issue falls into family planning, which is allowed by Sharia. However, this is provided that the device is inserted by a female doctor and that it doesn`t cause harm to the woman. And Allah The Almighty Knows Best.
Where should a woman who is led by her husband in prayer stand?
All perfect praise be to Allah The Lord of The Worlds It is from Sunnah (Prophetic tradition) that she stands behind him. And Allah Knows Best.