Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
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.
What is the ruling on looking at pictures of naked women via the internet?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is impermissible to look at pictures of naked women via the internet, and this act is forbidden according to Sharia. The proof of this is that Almighty Allah Says (What means): "Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: And God is well acquainted with all that they do." [An-Nur/30]. Therefore, we advise you to busy yourself with offering acts of obedience that draw you closer to Allah and prepare yourself for meeting Him on The Day of Judgment. And Allah The Almighty Knows Best.
How is night prayer offered?
Night prayer is offering voluntary prayer after Maghrib and before Fajr (Dawn). As for Tahajjud, it is offering voluntary prayer at night after waking up voluntarily, and for Allah`s sake as He Says (What means): "And pray in the small watches of the morning: (it would be) an additional prayer (or spiritual profit) for thee: soon will thy Lord raise thee to a Station of Praise and Glory!" [Al-Isra`/79]. Offering Tahajjud is better than offering voluntary prayer before going to bed.