Dought & clear, - Naafil prayers at times when prayer is notallowed. - (Prostration when reading Qur’aan and Prostration of thanksgiving)

When the sun rises and sets, are all naafil prayers forbidden, even
two rak'ahs for seeking forgiveness and the tworak'ahs following
tawaaf and the prostration of recitation? What is the evidence for
that?.
Praise be to Allaah.
Firstly:
We have already discussed the issue of naafil prayers at times when
prayer is forgiven.Please se questions no. 306, 8818and 20013.
Secondly:
The prostration of recitation is not prayer according to the more
correct of the two scholarly opinions. We have already discussed this
in questions no. 4913and 22650.
Based on this, it is permissible to prostrate when reading one of
theQur'aanic verses where prostration is required at times when prayer
is not allowed, according to the more correct of the two scholarly
views, because that does not come under the same rulings as prayer.
Even if we assume that it does come under the same rulings as prayer,
it is permissible to do it at times when prayer is otherwise not
allowed because it is something that is done for a reason,like the
eclipse prayer, and the two rak'ahs following tawaaf if one has done
tawaaf at a time when prayer is not allowed.
Fataawa al-Lajnah al-Daa'imah, 7/264.
Thirdly:
Your saying, "the two rak'ahs for seeking forgiveness"; perhaps what
you mean is the two rak'ahs of repentance, which are prescribed when
repenting from sin. It was narrated that Abu Bakrah (may Allaah be
pleased with him) said: I heard the Messenger of Allaah(peace and
blessings of Allaah be upon him) say: "There is no man who commits a
sin then he gets up, purifies himself and prays two rak'ahs, then asks
Allaah to forgive him, but Allaah will forgive him." Then he recited
this verse (interpretation of the meaning):
"And those who, when they have committed Faahishah (illegal sexual
intercourse) or wrongedthemselves with evil, remember Allaah and ask
forgiveness for their sins; — and none can forgive sins but Allaah
—and do not persist in what (wrong) they have done, while they know"
[Aal 'Imraan 3:135]
Narrated by al-Tirmidhi, 408; Abu Dawood, 1521; Ibn Maajah, 1395.
Classed as saheeh by al-Albaani inSaheeh Abi Dawood, 1346.
The two rak'ahs of repentance constitute a prayer for which there isa
reason, so it is permissible to do that at a time when prayer is
otherwise not allowed. And Allaah knows best.
In other saheeh reports there are other descriptions of the two
rak'ahs which expiate for sin. This may be summed up as follows:
-There is no one who does wudoo' and does itwell (because sins come
out from the washed limbs with the water or with the last drop of
water)
Part of doing wudoo' well is to sayBismillaah(In the name of Allaah)
before starting it, and reciting dhikr after it, as follows:Ashhadu an
laa ilaaha ill-Allaah wahdahu laa shareeka lah, wa ashhadu anna
Muhammadan 'abduhu wa rasooluhu. Allaahumma aj'alni min al-tawwaabeena
waj'alni min al-mutatahhareen. Subhaanaka Allaahumma wa bi hamdika,
ashhadu an laailaaha illa anta, astaghfiruka wa atoobu ilayk(I bear
witness that there is no god but Allaah alone, with no partner or
associate, andI bear witness that Muhammad is His slave and Messenger.
O Allaah, make me one of those who repent and make me one of the
purified. Glory and praise be to You, O Allaah, I bear witness that
there is no god but You, I seek Your forgiveness and I repent to You).
This dhikr recited after wudoo' brings a great reward.
-Then he gets up and prays two rak'ahs
-In which he does not make any mistake
-And does not let his mind wander
-And he remembers Allaah and focuses with proper humility
-Then he asks Allaah to forgive him
The outcome will be: that he is forgiven for his previous sins and
willdeserve Paradise.
Saheeh al-Targheeb, 1/210-211.