What is the ruling on working for a company that manufactures cigarettes?

All Perfect Praise is due to Allah, The Lord of The Worlds

Working for a company that manufactures cigarettes is forbidden because smoking itself is forbidden, so its production, selling and circulation are forbidden as a result since they aid in committing sin, and whoever aids in that is like the sinner himself. And Allah Knows Best.

I took a car from the Orphans' Fund Development Institution; is there usury (Riba) involved in this transaction?

If the Sharia's conditions were met, then there is no harm in this. And Allah The Exalted Knows Best.

What is the ruling on reciting the Chapter after Al-Faatihah , and what should a worshiper who forgets it do?

All perfect praise be to Allah, The Lord of The Worlds.                                                                                                                                                                  Any other part of Qur'an that a worshiper reads after Al-Faatihah during the first and the second Rak`ahs is a Sunnah, and forgetting to do so doesn`t nullify prayer, and doesn`t require performing Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.

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.