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.

Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?

It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.

What should a person who was favored from Allah with a newborn, but couldn`t afford an Aqeeqah, do?

Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) is a desirable Sunnah for the financially able since Allah, The Exalted, charges not a soul beyond its capacity. Therefore, if the father couldn`t afford the Aqeeqah before the end of his wife`s confinement, then it isn`t due on him, and if he was able to afford it later on, then it is permissible, but if he didn`t until the child reached puberty, the latter can offer the Aqeeqah himself.

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.