All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
There is no harm in reciting one of the Soorahs or verses that are recited in the Ruqyah (Quranic healing) in the prayer. The Prophet, sallallahu ‘alayhi wa sallam, approved the action of the Companion who used to recite Soorah Al-Ikhlaas (no. 112) in all the prayers because he loved it. ‘Aa'ishah, may Allah be pleased with her, narrated that the Messenger of Allah sent a man in charge of an expedition and that he would recite for his Companions during their prayer, ending (his recitation) with Soorah Al-Ikhlaas. When they returned, they mentioned it to the Messenger of Allah, sallallahu ‘alayhi wa sallam, so he told them to ask him why he was doing that. So they asked him, and he said, "Because it is the description of The Most Merciful (Allah), and (for this reason) I love to recite it." The Messenger of Allah, sallallahu ‘alayhi wa sallam, thereupon said, "Inform him that Allah loves him." [Al-Bukhari and Muslim]
Ibn Al-‘Arabi commented on the hadeeth, saying, "It is deduced from this hadeeth that it is allowable to repeat the same Soorah in each Rak‘ah (unit of prayer) of the prayer."
Ar-Ruhaybaani wrote about reciting supplications in the prayer:
"There is no harm if he recites a supplication from the Quran, such as the verse: {Our Lord, give us in this world (that which is) good and in the Hereafter (that which is) good and protect us from the punishment of the Fire.} [Quran 2:201] or a supplication from the Sunnah, or he seeks refuge with Allah by means of the Quran from evils such as fever, because it is Quran that is recited for a purpose that befits it, and it does not contradict the prayer. This is like the case of someone who recites the Faatihah with the intention of fulfilling the obligation of reciting it in the prayer as well as deriving blessings from it." [Mataalib Uli An-Nuha]
As for reciting different verses from different Soorahs in the same Rak‘ah, the apparent view of the scholars is that it is disliked. Al-Kharashi said, "If he moved from one Soorah to another, he is not required to perform Sujood Sahw (prostration of forgetfulness); however, he should not do so deliberately." [Sharh Mukhtasar Khaleel, 1/316]
Al-Hattaab said, "If he forgetfully moved from one Soorah to another, he bears no sin because he has not recited something that is alien to prayer. At-Tilmisaani said in Sharh Al-Jallaab, 'If he did so deliberately, it is disliked, because it involves reciting the Quran out of sequence and may cause confusion to the listener...'" [Mawaahib Al-Jaleel fi Sharh Mukhtasar Khaleel, 2/23]
Al-Muheet Al-Burhaani fi Al-Fiqh An-Nu‘maani (1/304) reads, "If he moves from one verse to another verse from another Soorah or from the same Soorah but separated from the first verse by other verses, it is disliked. It was authentically reported that the Prophet, sallallahu ‘alayhi wa sallam, forbade Bilaal, may Allah be pleased with him, from doing this when he heard him moving from one Soorah to another. He said to him, 'Recite each Soorah in its correct order."
Ibn Al-Humaam said, "It is disliked to move from a verse in a Soorah to a verse from another Soorah and from one Soorah to another Soorah that is separated from the first by one or more Soorahs in the same Rak‘ah... If he intended to recite a Soorah and started another (by mistake) so he left it and started the Soorah he intended, this is disliked even if he had recited only one letter of that Soorah..." [Fat-h Al-Qadeer]
Allah knows best.