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 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.
A person is sponsoring an orphan and pays the sponsorship monthly. Is it permissible to pay this month's sponsorship from zakat money?
It is permissible to pay the orphan's sponsorship from zakat money if the orphan is poor and has no one to support them. The person must intend to count it as part of their zakat when paying the money. And Allah Knows Best.
Is it permissible for the woman to use her mobile phone while on the street?
All Perfect Praise is due to Allah, The Lord of The Worlds
Modesty should be observed by the woman at all times, so she is free to use her phone while on the street as long as it is done within the limits of Islamic manners. And Allah The Almigty Knows Best.