Which are the quran surah and ayats that every single muslim should memorize them.and what the sunnah which every muslim should know and perform them.
Some Islamic knowledge is obligatory for every accountable individual to learn. This is called fard ‘ayn (individual obligation). The definition is: if it has to do with an act of worship that he is obliged to do, or a transaction that he wants to engage in (then he must learn it).
And some knowledge is obligatory for the ummah in general: if some of them do it in the required manner then the rest are absolved of responsibility, otherwise all of those who are able to do it are sinning. This is called fard kifaayah (communal obligation).
Memorizing Qur’aan and hadeeth comes under the leading of the latter. The ummah is obliged to preserve the Book of Allaah and the hadeeth of His Messenger, whether in their hearts or on paper, so that nothing of the two sources of legislation will be lost. Imam al-Nawawi (may Allaah have mercy on him) said in the introduction to Sharh al-Muhadhdhab (1/51): The second type – i.e., of Islamic knowledge – is a communal obligation (fard kifaayah), which means acquiring that Islamic knowledge which is essential for the people to establish their religion, such as memorization of Qur’aan and hadeeth, and their sciences, and usool al-fiqh.
As for memorization of Qur’aan and hadeeth as an individual obligation – i.e., that which the accountable Muslim is required to memorize – he is not obliged to memorize any of that by heart, he only has to memorize that without which prayer is not valid. Al-Faatihah has to be learned by every accountable person, i.e., he has to learn how to recite it properly. If he learns it by heart that is good; if he does not learn it by heart then he must read it from the Mus-haf or a piece of paper and the like.
Al-Nawawi said in al-Majmoo’ (3/335): Our companions said: If a person is not able to recite al-Faatihah then he should acquire the ability to do so by learning it, or acquire a Mus-haf from which he can read it, by buying it or renting it or borrowing it. If he is praying at night or in the dark, then he must acquire a lamp if he can. If he refuses to do that when he is able to do it, then he is sinning and must repeat every prayer that he offered before he learned al-Faatihah. Our evidence is the well-known shar’i principle that everything without which an obligatory duty cannot be performed, when it is within a person’s capabilities, is obligatory. End quote.
In Kashshaaf al-Qinaa’ (1/34) by al-Bahooti (may Allaah have mercy on him) it says: “The ignorant person” i.e., the one who cannot recite al-Faatihah well “must learn it” because it is obligatory in prayer, so he has to learn it if he is able to, as a condition (of prayer). “If he does not do that” i.e., if he does not learn al-Faatihah, “when he is able to do it, then his prayer is not valid” because he has failed to do an obligatory action when he was able to do it. End quote.
Mustafa al-Ruhaybaani al-Hanbali said in Mataalib Ooli al-Nuha (1/432): The ignorant person must learn al-Faatihah because it is obligatory in prayer, so he must learn it if he is able, as it is a condition of prayer. End quote.
The same applies to hadeeth: Muslim men and women are not required to memorize any of them, but it is essential to learn that without which the prayer is invalid, such as the hadeeth which describes the wording of the tashahhud to be recited in prayer. Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (1/315): The minimum that is acceptable is Al-Tahiyyaatu Lillaahi wa’l-salaamu ‘alayka ayyhuha’l-nabiyyu wa rahmat-Allaah, al-salaamu ‘alayna wa ‘ala ‘ibaad Illaah il-saaliheen, ashhadu an la ilaaha ill-Allaah wa ashhadu anna Muhammadan ‘abduhu wa rasooluhu (or anna Muhammadan rasool-Allaah) [All compliments are due to Allaah, Peace be upon you, O Prophet, and the mercy of Allaah, Peace be upon us, and on the righteous slaves of Allaah. I bear witness that there is no god except Allaah, and I bear witness that Muhammad is His slave and Messenger (or that Muhammad is the Messenger of Allaah)].”
And Allaah knows best.