Answered by Shaykh Abdurrahman ibn Yusuf Mangera
In the name of Allah the Inspirer of truth
1. Your method and order of supplications seems fine. May Allah reward you and accept your worship.
2. One can make du'a both immediately after the fard prayer (as in Fajr and 'Asr) or wait until after the supplementary prayers are completed. It states in the Fatawa Hindiyya that aside from the du'a Allahumma anta ’s-salam wa minka ’s-salam… one should get up to perform his supplementary prayers, hence, that would be recommended in Zuhr, Maghrib, and 'Isha', but not necessary.
3. If one is performing witr prayer with the 'Isha' prayer, then the du'a can be made after the witr. If, however, the witr is being delayed until one wakes up for tahajjud then a du'a would be recommended after 'Isha' to benefit from the promised acceptance of du'as after fard prayers, and then another du'a at tahajjud time to benefit from the blessings of that part of the night.
Abu Umama (may Allah be pleased with him) said that the Messenger of Allah (upon him be peace) was asked: "At what time does the supplication find the greatest response?'' He (upon him be peace) replied, "A supplication made during the middle of the last part of the night and after the conclusion of the obligatory prayers'' (Tirmidhi).
4. From Reflections of Pearls (to be published soon).
Prayers to be read after the obligatory (fard) prayers
First recite the prayer for forgiveness (istighfār) thrice,
I seek forgiveness from Allāh.
اَللّٰهُمَّ أَنْتَ السَّلاَمُ، وَمِنْكَ السَّلاَمُ، تَبَارَكْتَ يَا ذَا الْجَلاَلِ وَالْإِكْرَامِ
 Allāhumma Anta’s-Salām(u), wa minka ’s-salām(u), tabārakta yā Dha ’l-jalāli wa ’l-ikrām(i).
O Allāh, You are the Giver of Peace and peace comes from You alone. You are blessed, O Majestic and Benevolent (Muslim).
لاَ إِلٰهَ إِلَّا اللهُ وَحْدَهُو لاَ شَرِيْكَ لَهُو، لَهُ الْـمُلْكُ وَلَهُ الْحَمْدُ وَهُوَ عَلٰى كُلِّ شَيْءٍ قَدِيْرٌ.
اَللّٰهُمَّ لاَ مَانِعَ لِمَا أَعْطَيْتَ، وَلَا مُعْطِيَ لِمَا مَنَعْتَ، وَلَا يَنْفَعُ ذَا الْجَدِّ مِنْكَ الْجَدّ
Lā ilāha illa ’Llāhu wahdahū lā sharīka lah(ū), lahu ’l-mulku wa lahu ’l -˙amdu wa Huwa çalā kulli shay’in Qadīr(un). Allāhumma lā māniça limā aç†ayt(a), wa lā muç†iya limā manaçt(a), wa lā yanfa-çu dha ’l-jaddi minka ’l-jadd(u).
There is no god but Allāh, He is One, He has no partner. His is the Sovereignty and His is all praise. He has power over all things. O Allāh, none can withhold that which You bestow and none can bestow that which You withhold and the wealth of the wealthy cannot help them from You [i.e. Your wrath and punishment] (Bukhārī, Muslim).
سُبْحَانَ اللهِ Sub˙ān Allāh(i) (Exalted is Allāh), and اَلْحَمْدُ للهِ Al-˙amdu li ’Llāh(i) (Praise be to Allāh) thirty three times, then say: اللهُ أَكْبَرُ Allāhu akbar(u) (Allāh is the Greatest) thirty four times (Bukhārī, Muslim).
A special prayer to be recited after Fajr and Maghrib
Recite 7 times:
اَللّٰهُمَّ أَجِرْنِيْ مِنَ النَّار
ِ Allāhumma ajirnī mina ’n-nār(i). O Allah, save me from the Fire (Abū Dāwūd).
Abdurrahman ibn Yusuf
MMVIII © Qibla.
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