"And during part of the night forsake sleep by prayer, beyond what is incumbent on thee; maybe thy Lord will raise thee to a position of great glory" (17:79).
"The rising by night is the firmest way to tread and the best corrective of speech" (73:6).
"Surely thy Lord knows that thou passest in prayer nearly two-thirds of the night, and (sometimes) half of it, and (sometimes) one-third of it, and also a part of those who are with thee" (73: 20).
Tahajjud, from hajada meaning he remained wakeful in the night, is the prayer which is offered during the latter part of the night, before daybreak. It is a supererogatory prayer, but special stress is laid on it in the Holy Qur'ān (vv. 1, 2). Witr, (lit. an odd number), originally a part of the Tahajjud prayer. is a supererogatory prayer of three rak'ahs, generally said after the 'Isha' prayer. Tarāwīh (pl. of tarwihah meaning rest) is a supererogatory prayer of eight or twenty rak'ahs said during the month of Ramadhān immediately after the 'Ishā' prayer.
The Tahajjud prayer is said, after one has enjoyed sleep, during the latter third of the night (h. 1), This prayer consists of eleven rak'ahs (h. 2). but may be shortened to nine or seven or even less (hh. 3. 4), there being a break after every two rak'ahs. As all people could not afford to get up in the latter part of the night, three rak'ahs of witr were added to the 'Ishā' prayer, being the final act of devotion before going to sleep (hh. 5, 6). The last rak'ah of witr wascharacterized by a special prayer offered before or after Rukū' and called the Qunūt
The Tarāwīh prayer really takes the place of Tahajjud, in the case of those who cannot get up for Tahajjud, in the month of Ramadhan. In its present form, it was introduced in the time of 'Umar
Abn Hurairah reported,
The Messenger of Allāh,S.A.W said,
"Our Lord, blessed and exalted is He, descends every night to the nearest heaven when the latter one-third of the night remains, (and) says, Is there any one who calls upon Me so that I may accept of him, who asks of Me so that I may grant him, who seeks forgiveness of Me so that I may forgive him?
If you forgot to Surah after Al-Fatihah, then you must re-do that Salah again
and remember you dont have to say any other Surah at 3rd and 4th Rakah be it Olibgatory or Non-Obligatory.
to your B question
not mine Fatwa from Islamweb.net
It is permissible to offer supererogatory prayers in congregation according to the majority of scholars.
Ibn Qudama said in Al-Mughni: "It is permissible to offer supererogatory prayers individually or in congregation because the Prophet (Sallallahu Alaihi wa Sallam) did that both ways. However, most of his supererogatory prayers were performed individually. Once he prayed with Hudaifa, and once he prayed with Ibn Abbas, and one time he prayed with Anas and his mother, and an orphan. And once he led the prayer in the house of Ithban and the companions prayed behind him, and he led them in prayer as well during Ramadan three times."
Sheikh al Islam Ibn Taimiyyah said in Majmo'u Al fatawa 23/111: "The correct opinion is what is reported in the Sunnah, that it should not be disliked to perform supererogatory prayers in congregation as the Prophet (Sallallahu Alaihi wa Sallam) did so, and we should not make it as a proved Sunnah that should not be neglected like those who appoint an imam to pray these prayers between Magrib and Isha, or in the night continuously, in the same way that he leads them in the five obligatory prayers."
So if someone sometimes prays the night prayer, or unconditional supererogatory prayer in congregation, and does not perform it continuously, then it is acceptable.
As regards, the supererogatory prayers performed after or before obligatory prayers, or Istikharah prayer and a prayer that has a reason to be performed for, like the prayer after Wudu, the prayer of salutation to the mosque, and the like, then it is more appropriate to perform them individually.
Allah knows best.
and Wa Salam May Allah`s Peace be upon you too