I have several doubts regarding your question. However, I understand that it broadly means how is the texts (primary and secondary sources) handled in Islam and how explanations are made. I will give a brief explanation and I hope I answer your question as well, Insha Allah.
Qur'an: As for the text of the Qur'an itself, it is preserved as it was revealed. We believe Qur'an is the uncreated speech of Allah. You might want to read how Qur'an is preserved here.
EDIT: Now, that I understand what "textual criticism" is, I wanted to add a little bit about "Ahruf of the Qur'an" :
The ahruf are the various ways that the verses of the Qur’aan are read. Imaam al-Qurtubee (d. 671 A.H.) said,
“Every variation of a word in the Qur’aan is said to be a harf. So,
for example, when we say the harf of Ibn Mas’ood, it means the way
that Ibn Mas’ood used to recite that verse or word.”
The Qur’aan was revealed in seven ahruf.
The different ahruf are all directly from Allaah, and not from the Companions. The reason the Prophet (PBUH) requested the number of ahruf to be increased was to make the memorisation and recitation of the Qur’aan easier. However, this is just style of reading and that doesn't change the meaning of the Qur'an. There are different opinions as to what those seven ahruf are. Some say, the seven ahruf refer to the seven dialects (lughaat) of the Arabs prevalent at the time of the Prophet (salallahu alayhi wassalam).
As for today, the question is if the seven ahruf exists and there are many opinions on this. The Qur'an we have today is that compiled by Uthmaan (radiallahu anhu). You can read how he compiled in the link before. According to at-Tabaree (a scholar) and those who follow his opinion, ‘Uthmaan preserved only one harf. According to him, The seven ahruf were revealed by Allaah during the time of the Prophet (PBUH) to facilitate the memorisation of the Qur’aan, since the dialects of the Arabs were many. This facilitation (i.e., the ahruf) was not necessary to preserve, and eventually there was no need of it.
Second group of scholars hold the opinion that all of the ahruf are in existence today, and the mus-haf of ‘Uthmaan was written to preserve all seven ahruf.
The third group of scholars is composed of Ibn Taymiyyah (d. 724 A.H.), ash-Shaatibee (d. 790 A.H.), ar-Raazee (d. 606 A.H.), Ibn Katheer (d. 774 A.H.), Ibn al-Jazaree (d. 832 A.H.) and others. They argue that ‘Uthmaan preserved the ahruf to the extent that the script of his mus-haf allowed him to do so. Thus, these scholars hold that a portion of the seven ahruf are preserved.
As for interpretation and explanation of Qur'an, we call it tafseer. But, even tafseer has some principles as to how the text should be interpreted. The interpretation has several sources. The first source that must be used to interpret the noble Qur’aan is the Qur’an (itself) along with the Sunnah, which consists of the Prophet’s statements, actions and silent approvals. Then after that, it must be interpreted using the interpretations (tafseer) of the people of knowledge, at the head of whom are the Companions of the Prophet (sallAllaahu 'alayhi wa sallam). And the foremost amongst the Companions with regard to this subject (tafseer) is ‘Abdullaah bin Mas’ood (radyAllaahu ‘anhu). This is due to several factors, one being that he was one of the first to accompany the Prophet (sallAllaahu 'alayhi wa sallam) (i.e. accept Islaam), and another being that he (radyAllaahu ‘anhu) would give strong emphasis to asking about, understanding, and interpreting the Qur’aan. Then after him comes ‘Abdullaah bin ‘Abbaas (radyAllaahu ‘anhu), about whom ‘Abdullaah bin Mas’ood (radyAllaahu ‘anhu) said: “He is the interpreter (turjumaan) of the Qur’aan.”
Then after them, any Companion whose interpretation (tafseer) of an ayah (verse) can be authentically confirmed – and there exists no difference of opinion amongst the Companions regarding it, we accept this interpretation (tafseer) from him with full contentment, submission and reliance. And if no such tafseer can be found (from the Companions) regarding a particular ayah, then we take its tafseer from the Taabi’een (generation after the Prophet), particularly those who specialized in studying tafseer under the Companions of Allaah’s Messenger (sallAllaahu 'alayhi wa sallam), such as Sa’eed bin Jubair, Taawoos and others who are well known for their studying of tafseer under some of the Companions, particularly Ibn ‘Abbaas (radyAllaahu ‘anhu), as we mentioned previously.
So, even there are modern accepted tafseers, they do not deviate much from these explanation even though they have some opinions included it them. However, the majority explanation doesn't deviate at all.
Hadith: Sunnah is not text. Sunnah consists of the Prophet’s statements, actions and silent approvals. And we know Sunnah from Hadith. And these hadiths are passed down to us through various narrators who heard the Prophet's statements or saw his actions and approvals. So, there are several narrators who hear it from others and pass down to others. So, that makes a chain of narrators. And the chain goes back to the person who heard it from the Prophet (salallahu alayhi wassalam) himself.
There is a process of authentication of hadiths and we call it sciences of Hadith. A hadith is composed of three parts - Matn (text), isnad (chain of reporters), and taraf (the part, or the beginning sentence, of the text which refers to the sayings, actions or characteristics of the Prophet (Sallalaahu Ala'hi wa Sallam), or his concurrence with others action). The authenticity of the hadith depends on the reliability of its reporters, and the linkage among them. Based on the reliability and memory of narrators, Nature of the text and its chain, number of reports of the same hadith, and several criteria like that, we have classification of hadeeth. A hadith which is completely sound is called "sahih" and most rulings are derived from it. You can read requirements of sahih hadith here. And there is a field in science of hadith called Jarh wa Ta'deel (criticism and praising of hadith narrators). This is used to authenticate the hadith as well. It is a science where the scholars judge the uprightness, honesty and reliability of a hadith narrator which helps in authenticating the text.
So, this very short introduction to fundamentals of these sciences. However, it involves more deep concepts (which is studied at university level). The people who can do authentication undergo years of serious study before they do this and they are called Muhaddith and most Muhaddith are also faqih (scholars of Islamic jurisprudence).
Source and more: An Introduction to the Principles of Tafseer
Tayseer Mustalah-il-Hadeeth
The Ahruf of The Qur'an
