Do Anglicans believe the decision on the 66 book canon was infallible? Do Anglicans believe that the decision taken on the 66 book canon was an infallible decision? (like the attitude the Catholic Church has to the definition of the Canon in the Council of Trent).

If so, then do they still call to these people, organization(s) or decision-making process for more infallible decisions?

If not, how can we know the inspiration of a book isn't just an inappropriately high opinion of scholars and early Christians?
Disclaimer: this answer is based on my speculation from rudimentary knowledge of Anglicanism, but hopefully backed by sources.
TL;DR
No, because the canon has never being infallibly defined by the Church. Such definition requires a General Council, and to define truths that are held as such by all. No General Council (last one being in 680 AD) defined the canon. It follows that the decision of considering a particular canon is indeed the opinion of scholars/theologians.

Your question requires an understanding of what infallibility is according to Anglicanism. I found an excellent analysis of this in this book by the Anglican Bishop A.N. Littlejohn. It's a book from 1892, but still very insightful.
In essence, he states that the Catholic (i.e Universal) Church is infallible when it has declared in a General Council truths that had been accepted &quot;always, everywhere and by all&quot; (semper, ubique, et ab omnibus). Quoting in extenso from Chapter 1:

But whatever this authority in kind or in degree, in accordance with a fundamental rule of Catholic practice, it has always been exercised through General Councils. It is important, therefore, to have clear views not only of the authority itself, but also of the organ through which it has spoken. Now though in the strict sense of the terms general, universal, (Ecumenical are the same, yet the term (Ecumenical has been declared by usage to mean a General Council, lawful, approved, and received by all the Church.&quot; A council may be general without being lawful; to be general, all the bishops of the world should be summoned to it, and no one excluded save the heretical and ex- communicated. This rule was absolutely observed in none of the so-called General Councils, and only a minority of bishops sat in most of them. To be lawful and truly Oecumenical it is necessary that all that occurs should be done regularly (which was not the case with some of the General Councils), and that the Church at large should accept its decrees, as was done with those of the Councils of Nice, Constantinople, Ephesus and Chalcedon. That a General Council be accepted, it is not required that all the faithful individually considered acquiesce in its action. It suffices for the purpose that all branches of the Church do so in their corporate capacity. ... It has always been held that it is the duty of a Council to declare what has been the faith from the beginning, not to put forth new objects of belief. It might, on any given matter, develop implicit into explicit faith; but it was required to show that the matter so developed was a portion of the original deposit and revelation. But it is a fact, of which ecclesiastical history furnishes abundant evidence, that General Councils may err and sometimes have erred in things pertaining to God. &quot;The inerrancy of a council can never be guaranteed at the moment. The value of a council is tested by its after reception by the Church.&quot;

Thus, for Anglicanism, only the four ecumenical councils listed above are regarded as infallible (according to Anglicanism, the last General Council was that of 680; see page 27 of book). It follows then that the 397 AD Council of Carthage, which (as guest37 said) was the first council to define the canon of the Bible (canon that included the apocrypha), is not considered infallible in Anglicanism (not the least because it was not a General Council). Neither of the four councils above defined the canon.
So, first conclusion is &quot;the canon with apocrypha was not infallibly defined by the Church&quot;.
The second part of the argument follows through. The same author of the book above states:

The last undisputed General Council was held at the close of the seventh century (680). Is it true, then, that the Church's only duly accredited organ for defining and formulating truth has been in abeyance for 1200 years, or since the great schism between the East and West? If it be true, the consequences are not so grave as some would have us think. The suspended exercise of one form of the Church's authority does not involve the suspension of her authority in other forms. In spite of this she may still do her work as the ecclesia docens, and in various ways enjoy the benefits of the Spirit's guidance into all truth necessary to salvation; still it is, indeed, a startling fact that her plenary power for deciding controversies should have been for so many centuries powerless. What inward lesions and outward assaults may have come upon her, because of this dormant function only her own eternal Head can surely know. Certain it is that, while schism continues to do its will upon the torn body, the power of inerrancy inherent only in the united whole cannot be set in motion. All that has been decreed in any one of the hundred parts is liable to revision, and the guidance so freely promised to the Universal Episcopate must be greatly narrowed as to its present use.

It then follows that, for Anglicanism, the canon of the Bible has not been infallibly defined by the Church. This is all the more obvious from the very fact that infallibility requires acceptance semper, ubique, et ab omnibus. It is evident that such is not the case by the canon. Hence, it is not possible for the 66 book canon to be defined as infallible.
Beside this, the Anglican Church has its own position on the subject, which is however fallible. Articles II and III in Chapter I of the Westminster Confession of Faith states:

II. Under the name of Holy Scripture, or the Word of God written, are now contained all the books of the Old and New Testament, which are these: Of the Old Testament: Genesis, Exodus, Leviticus, Numbers, Deuteronomy, Joshua, Judges, Ruth, I Samuel, II Samuel, I Kings, II Kings, I Chronicles, II Chronicles, Ezra, Nehemiah, Esther, Job, Psalms, Proverbs, Ecclesiastes, The Song of Songs, Isaiah, Jeremiah, Lamentations, Ezekiel, Daniel, Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zechariah, Malachi. Of the New Testament: The Gospels according to Matthew, Mark, Luke, John, The Acts of the Apostles, Paul's Epistles to the Romans, Corinthians I, Corinthians II, Galatians, Ephesians, Philippians, Colossians, Thessalonians I , Thessalonians II , To Timothy I , To Timothy II, To Titus, To Philemon, The Epistle to the Hebrews, The Epistle of James, The first and second Epistles of Peter, The first, second, and third Epistles of John, The Epistle of Jude, The Revelation of John. All which are given by inspiration of God to be the rule of faith and life.
III. The books commonly called Apocrypha, not being of divine inspiration, are no part of the canon of the Scripture, and therefore are of no authority in the Church of God, nor to be any otherwise approved, or made use of, than other human writings

In conclusion, and assuming the position by the Anglican Bishop in the book is that of the Anglican Church, the answer to your question is no. From here it follows that the decision of considering a particular canon is indeed the particular opinion of Anglican scholars/theologians.