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 is His slave and Messenger.
First of all, you should take it easy and we hope that such narrations would not be a source of disturbance to you.
There is no doubt that the Quran is preserved by Allah Almighty, as He has undertaken its preservation Himself. Allah Says (what means): {Indeed, it is We who sent down the Quran and indeed, We will be its guardian.} [Quran 15:9]
The consensus of the Muslim scholars that Allah preserved the Quran was quoted by different scholars. Al-Qaadhi ‘Iyaadh said in his book Ash-Shifa:
"Muslim scholars have agreed that the Quran which is recited in all the regions of the world and which is written in the Mus-haf (the hardcopy of the Quran) by the hands of the Muslims, starting with the first (chapter in its) cover, ‘Al-Hamdu Lillahi Rabi ‘Aalameen’ (Al-Faatihah) to the last (chapter in its) cover, Qul ‘A’oothu bi Rabbi An-Naas’ (An-Naas), is the words of Allah, and it is a revelation revealed to His Prophet Muhammad and that all which it contains is the truth...” [End of quote]
With regard to the quote of Ibn ‘Umar we did not find any scholar who stated whether it is authentic or inauthentic. Even if we presume that it is authentic, then it would be referring to the verses the recitation of which was abrogated from the Quran. This is the context in which As-Suyooti reported this quote in his book Al-Itqaan as he said: (The third type is that which its recitation has been abrogated but not its ruling) and also he mentioned other statements (quotes).
What was stated by As-Suyooti was also mentioned by Al-Aloosi in his Tafseer entitled Rooh Al-Ma’aani as he said:
"The scholars have agreed in consensus that there is no deficiency in the Quran which was conveyed as Mutawaatir, as is found between the two covers [of the Book] today. Indeed, at the time of Abu Bakr As-Sideeq, what was not agreed to be Mutawaatir was left out as well as anything the recitation of which has been abrogated, although it was recited by those who were unaware of its abrogation. Additionally, anything which was not included in the last review (of the Quran) was also left out ….." [End of quote]
On the other hand, Ibn Hajar said in his book Fatah Al-Baari that the statement of ‘Umar was interrupted (in the chain of narration), i.e., it is inauthentic. The report does not mention that it was lost. The wording of the report is as follows:
"From Al-Hasan, it was reported that ‘Umar ibn Al-Khattaab asked about a verse from the Book of Allah, and it was said to him: It was with so and so who was killed in the battle of Al-Yamaamah. Thereupon he said: ‘To Allah we belong’; and he ordered that the Quran be collected in one book and it was collected in one book, and he was the first one who collected it in one Mus-haf.”
However, it is known that Abu Bakr was the one who collected the Quran, unless the words ‘the first’ mean that ‘Umar was the first one to advise Abu Bakr to collect it [in one Mus-haf] as stated by Ibn Hajar in Fat-h Al-Baari.
Besides, this verse, which ‘Umar asked about, was recognized by those whom he asked. This proves that this verse was known to them, and that it is from the Quran. It could be that the one who was killed in the battle of Yamaamah was the one who learnt it from the mouth of the Prophet then others learnt it from him. All this, if we presume that the statement of the companion is authentic, but we have already mentioned that it is inauthentic.
Moreover, we have not come across the statement of Zuhayr to which you referred. Saying that something from the Quran was lost because of the reciters who were killed in Al-Yamaamah is a pure lie.
Those who memorized the Quran by heart were so many, among whom were the four caliphs themselves and so many other companions as mentioned by Az-Zarqaani in his book Manaahil Al-‘Irfaan.
With regard to the Mas-hafs that were in the hands of the Companions, then when ‘Uthman gathered the people upon one single Mus-haf; he ordered them to burn the other Mus-hafs they had with them, and they adhered to him.
Ibn Abu Daawood narrated in Al-Masaahif from Mus'ab ibn Sa'd ibn Abu Waqqas who said: “When ‘Uthmaan burned the Quran, there were so many people present and they liked what ‘Uthman did”, or he said: “No one objected to that”. Ibn Katheer said in his Tafseer (interpretation of the Quran): “This is an authentic chain of narration.”
What was narrated about Ibn Mas'ood that he refused that his Mus-haf be burned, then Az-Zarqaani said that he went back on his opinion when he realized the advantages of the Masaahif that were collected by ‘Uthmaan and the Muslims (Companions) agreeing to it and that it is a means of uniting them.
Additionally, the Quran used to be written and the Prophet had scribes who used to write down the revelation and he used to order them to write what was revealed to him.
In conclusion, the Quran was preserved by Allah as He promised, and the Muslim must believe in this, and he should not doubt it. One must also be careful of those who cast doubts about this issue and try to spread misconceptions to confuse the Muslims about their religion.
Allah knows best.