I work for a company whose manager refuses to allow employees to leave during work hours. Do I incur sin if I secretly went out to join the congregation at the Masjid? Is doing so considered a breach of trust?

Praise be to the Lord of the Worlds.

We recommend that you pray at work to encourage your colleagues to follow suit, because whoever guides to good has the like of the reward of the person who actually does it. And Allah The Almighty 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.

Is it permissible for a woman whose menses exceeded (15) days to pray, fast and do what was prohibited on her to do during the latter period?

If the menses exceeded 15 days then it is deemed menstruation, and in this case she is obliged to pray and fast and to do what was impermissible for her to do during the latter period. In addition, she is obliged to make an ablution for each obligatory prayer after it's due time and making sure that impuity is removed. Finally, your menstruation period is over (Questioner) simlar to your menstruation in the previos month.

Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?

Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.