Is it permissible for a suitor to go out with his fiancé upon the conclusion of the marriage contract?

Upon the conclusion of the marriage contract, the woman becomes lawful for her husband. However, the customary practice should be observed in this regard since rights could be lost in case of divorce, or death.

What is the ruling on praying behind an undesirable Imam?

It is permissible to pray behind an Imam who is undesirable for committing religious violations, and it is disliked for such an Imam to lead the prayer. Still, If he was undesirable for a personal, or a worldly matter, then such argument doesn’t hold water. And Allah Knows Best.

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 woman in her waiting period (Iddah) after her husband's death to leave her house and mix with non-Mahrams?

It is not permissible for a woman in her waiting period (Iddah) after the death of her husband to leave her house except for a necessity, such as for medical treatment, nor is she allowed to mix with non-Mahrams. A woman is not permitted to mix with anyone other than her husband or Mahrams, whether she is in her waiting period or not. However, there is no harm in accepting condolences from those who visit and responding to their inquiries about her well-being. And Allah Knows Best.