What is the ruling of Islamic Law on supplicating with other than the transmitted (Ma'thur) supplications in prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to supplicate (make du'a) during the prayer for anything from the affairs of religion or worldly life, and the prayer is not invalidated by doing so.
Shaykh al-Islam, the Imam an-Nawawi, may Allah have mercy on him, says: "Our madhhab [i.e., the Shafi'i madhhab] holds that it is permissible for a person to supplicate during it [the prayer] with anything that is permissible to supplicate with outside the prayer, from the affairs of religion or worldly life. He may say: 'O Allah, grant me wholesome sustenance, offspring, a house, and a beautiful young wife' — describing her; or: 'O Allah, free so-and-so from prison,' or 'destroy so-and-so,' and other such things — and none of this invalidates his prayer according to us. And this is also the view of Malik, ath-Thawri, Abu Thawr, and Ishaq." [Al-Majmu', Vol.3/P.454]. And Allah, the Exalted, knows best.
A man led the people in prayer as imam, and at the end of the prayer he performed a prostration of forgetfulness (*sujūd al-sahw*) because he had omitted a short *sūrah* after al-Fātiḥah. What is the ruling on his prayer and that of those praying behind him?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
According to the Shāfiʿī school, it is sunnah to recite a sūrah after al-Fātiḥah in the prayer. One who omits it has a valid prayer, and no prostration of forgetfulness (sujūd al-sahw) is prescribed for omitting it. If someone performs sujūd al-sahw for its omission while knowing the ruling and remembering it, his prayer is invalidated. But one who is ignorant of the ruling, or who did so out of forgetfulness, his prayer is not invalidated, because this is among the matters that are obscure to people, and ignorance of it is not restricted to those who recently entered Islam.
Shaykh al-Islām al-Shams al-Ramlī said in Nihāyat al-Muḥtāj ilā Sharḥ al-Minhāj (Vol.2/p.70): “The remaining sunnahs are not compensated for by prostration, such as the remembrances (adhkār) of bowing and prostration, that is, the opening supplication (duʿāʾ al-iftitāḥ) and the sūrah, in accordance with the base rule, because they are not of the same nature as what has been reported [as compensable]. If one prostrates for any of them deliberately, his prayer is invalidated, unless he is excused due to ignorance. As for the objection raised that the ignorant person does not know that sujūd al-sahw is prescribed, and whoever knows it knows its place, this is refuted by denying such a necessary connection, for the ignorant person may hear only that sujūd al-sahw is prescribed before the salām, and so assume that it applies to every sunnah and is not restricted to its prescribed place.”
This is among the matters that are obscure, in which the mukallaf is excused for ignorance, as stated by al-Shabrāmallisī in his Ḥāshiyah ʿalā Nihāyat al-Muḥtāj (Vol.2/p.70).
However, if the imam prostrates, and the follower (maʾmūm) presumes that his imam’s prostration is for a reason for which one does not prostrate, it is not permissible to follow him in it, so long as the follower knows the ruling.
Accordingly, the prayer of one who did not recite a sūrah after al-Fātiḥah is valid, and sujūd al-sahw is not prescribed for it. Whoever prostrates out of ignorance or forgetfulness, his prayer is valid, because this is among the issues hidden from the general public. But whoever prostrates while knowing the ruling and remembering it, his prayer is invalidated. And Allah Almighty knows best.
Should one who doesn`t perform prayer out of laziness make it up later, and how should he/she do so?
All perfect praise be to Allah,The Lord of The Worlds He/she is obliged to make up missed prayers by offering with each obligatory prayer another one, and if he/she offers two, then it is better. And Allah 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.