Offering supplication whilst reciting Quran
Question

I recite Quran, praise be to Allah, and when I reach a verse which describes the believers, I ask Allah to make me one of them;  and when I reach a verse that describes the disbelievers and hypocrites, and their fate, I seek refuge with Allah and ask Him not to make me one of them. After offering supplication, do I have to recite the Basmalah again, or can I resume reciting without that? Is it permissible to interrupt recitation in order to offer supplication?
Praise be to Allah.This is permissible, as the Prophet (blessings and peace of Allah be upon him) did it. When praying tahajjud at night, when he (blessings and peace of Allah be upon him) came to a verse that spoke of warning, he would seek refuge with Allah, and when he came to a verse that spoke of mercy, he would ask his Lord for mercy. So there is nothing wrong with that; in fact it is recommended when praying tahajjud at night, when praying by day, or when reciting Quran outside of the prayer. All of that is recommended, and you do not have to repeat the Basmalah or ta`awwudh [seeking refuge with Allah]; rather you may offer this supplication then resume reciting with no need to repeat the ta`awwudh or Basmalah. All of this applies if you are praying on your own, offering a supererogatory prayer.
But if you are offering an obligatory prayer, there is no proof that the Prophet (blessings and peace of Allah be upon him) did this in an obligatory prayer. The same applies if you are praying with the imam; you should listen attentively to your imam and not offer these supplications when the imam is reciting; rather you should remain silent and listen in prayers in which the recitation is done out loud. As for prayers in which recitation is done quietly, you should recite al-Fatihah and whatever else you can recite, without offering the supplications that may be offered during a supererogatory prayer, because the Messenger (blessings and peace of Allah be upon him) did not do that in the obligatory prayer. Perhaps the reason for that – and Allah knows best – was to make it easier for the people and not make the prayer too lengthy for them, because if he had offered supplication at every verse which mentions mercy and sought refuge with Allah at every verse that contains a warning, the prayer may have become very long, and perhaps that might have been difficult for the people. So by the mercy of Allah and His kindness towards His slaves, He did not prescribe that in the obligatory prayer, so that the recitation would be uninterrupted, and so that the recitation would not be too lengthy for the people. But in the case of supererogatory prayers or tahajjud or qiyam al-layl, or in Duha prayer and other supererogatory prayers, there is nothing wrong with that, and the matter is flexible. End quote.