What is the "fideism" rejected by the Catholic Church?

The very question biases all answers. Consider what St Thomas says -- and is proved by so many pagan philosophers

The existence of God and other like truths about God, which can be known by natural reason, are not articles of faith, but are preambles to the articles; for faith presupposes natural knowledge, even as grace presupposes nature, and perfection supposes something that can be perfected. Nevertheless, there is nothing to prevent a man, who cannot grasp a proof, accepting, as a matter of faith, something which in itself is capable of being scientifically known and demonstrated. (Summa Theologiae Ia, q. 2, a. 2, ad 1)

At its most wide sense, the teaching against Fideism actually says that nothing that is of faith is anti-rational, irrational. SO if reason can reach certain truths about God then all that is needed to get to the Creed is to say either

1. Jesus taught it so it must be true if He be the Son of God, or equivalently
2. If Jesus established a Church and the gates of Hell shall not prevail against it

and that that Church teaches X then X it is.

ONE CAUTION: A completely true belief can be misunderstood or believed on a wrong basis... and obviously what is of the Faith (De Fide, in the Creed) is what you believe. What fruit Eve ate can never be creedal even if you have absolute proof.

Fideists think faith is based on a feeling and not something that resides in the intellect.

Faith is the assent of the intellect to the truths* revealed by God**.
^{*Faith's material object    **Faith's formal object, the First Truth    (cf. the question "Whether the object of faith is the First Truth?")}

This assent requires absolute certitude, not probability:

• Vatican I Dei Filius ch. 3 "On Faith":

  the assent of faith is by no means a blind action of the mind

• condemned proposition in Pope St. Pius X's Lamentabili sane:

  25. The assent of faith ultimately rests on a mass of probabilities

• Sauvage, G. (1909), Fideism:

  before we believe in a proposition as revealed by God, we must first know with certitude that God exists, that He reveals such and such a proposition, and that His teaching is worthy of assent, all of which questions can and must be ultimately decided only by an act of intellectual assent based on objective evidence.

  These things are called the preambles of faith (præambula fidei), because they come before faith:

  The main premises of reason on which the act of divine faith depends as on its rational foundation. They are mainly three: 1. the existence of God; 2. his authority, or right to be believed because he knows all things and is perfectly truthful; and 3. the fact that he actually made a revelation, which is proved especially by miracles or fulfilled prophecies performed in testimony of a prophet's (or Christ's) claim to speaking in the name of God. (Etym. Latin praeambulus, walking in front: prae, in front + ambulare, to walk.)

• Catechism of the Council of Trent pt. 1 a. 1 "I believe…":

  Faith Excludes Doubt
  The knowledge derived through faith must not be considered less certain because its objects are not seen; for the divine light by which we know them, although it does not render them evident, yet suffers us not to doubt them. For God, who commanded the light to shine out of darkness, hath himself shone in our hearts (2 Cor. 4:6), that the gospel be not hidden to us, as to those that perish. (2 Cor. 4:3).

• ibid. "Necessity of Faith":

  That faith thus understood is necessary to salvation no man can reasonably doubt, particularly since it is written: Without faith it is impossible to please God. (Heb. 11:6). For as the end proposed to man as his ultimate happiness is far above the reach of human understanding, it was therefore necessary that it should be made known to him by God. This knowledge, however, is nothing else than faith, by which we yield our unhesitating assent to whatever the authority of our Holy Mother the Church teaches us to have been revealed by God; for the faithful cannot doubt those things of which God, who is truth itself, is the author. Hence we see the great difference that exists between this faith which we give to God and that which we yield to the writers of human history.²
  
  2. On the necessity of faith see Summa Theol. 2a. 2ae. ii. 3 ["Whether it is necessary for salvation to believe anything above the natural reason?"], 4 ["Whether it is necessary to believe those things which can be proved by natural reason?"].

Fideism, as Pascendi Dominici gregis §7 points out, results in thinking that faith is based on a sentiment or feeling,

without any prior judgment of the mind (nullo praevertente mentis iudicio).

According to Catholicism, in what matters is it legitimate to prioritize faith over reason?

All the truths you list above, which are beyond the capabilities of human reason alone to discover, can only be known through faith. See, for example: "Whether the trinity of the divine persons can be known by natural reason?" (Summa Theologica I q. 32 a. 1).

Just because there are truths beyond our human natural reason, that doesn't mean faith is not an intellectual virtue grounded in reason.

See: Summa contra Gentiles I ch. 6: "That to give assent to the truths of faith is not foolishness even though they are above reason".

An analogy: One wouldn't say that because calculus is beyond arithmetic that arithmetic is to be despised or is not necessary.

Problematic fideism in Catholicism occurs when faith is exalted at the expense of reason. That is, when faith involves or requires irrationality. Doctrines such as the Trinity are beyond reason and accessible only to faith, but they do not entail a transgression of reason. This can also occur in a lesser mode when appeals to faith downplay or undermine the role of reason. For example, John Paul II warns against privileging faith in scripture over the rationality of tradition and the Magisterium:

There are also signs of a resurgence of fideism, which fails to recognize the importance of rational knowledge and philosophical discourse for the understanding of faith, indeed for the very possibility of belief in God. One currently widespread symptom of this fideistic tendency is a “biblicism” which tends to make the reading and exegesis of Sacred Scripture the sole criterion of truth. In consequence, the word of God is identified with Sacred Scripture alone, thus eliminating the doctrine of the Church which the Second Vatican Council stressed quite specifically. Having recalled that the word of God is present in both Scripture and Tradition,73 the Constitution Dei Verbum continues emphatically: “Sacred Tradition and Sacred Scripture comprise a single sacred deposit of the word of God entrusted to the Church. Embracing this deposit and united with their pastors, the People of God remain always faithful to the teaching of the Apostles”.74 Scripture, therefore, is not the Church's sole point of reference. The “supreme rule of her faith” 75 derives from the unity which the Spirit has created between Sacred Tradition, Sacred Scripture and the Magisterium of the Church in a reciprocity which means that none of the three can survive without the others.76

Fides et Ratio, 55

John Paul II goes some way towards defining fideism when he quotes Dei Filius of the First Vatican Council. As noted above, problematic fideism is not the belief in the superiority of faith, but rather the belief that there can be a true divergence between faith and reason which results in a contradiction between the truths of faith and the truths of reason:

“Even if faith is superior to reason there can never be a true divergence between faith and reason, since the same God who reveals the mysteries and bestows the gift of faith has also placed in the human spirit the light of reason. This God could not deny himself, nor could the truth ever contradict the truth”.65

Fides et Ratio, 53