History of the doctrine of religious vocation in Catholic Church

1. "One should take long time to discern his religious vocation."

From Fr. William Doyle, S.J.'s Vocations:

7. Deliberation

It follows from what has been said that once the voice of God is recognized, that is when the thought of leaving the world has been more or less constantly before the mind for some time, and the souls realizes, even though she dreads it, that “the Lord hath need of her,” the call ought to be obeyed promptly.

St. Thomas [II-II q. 189 a. 10] holds that the invitation to a more perfect life ought to be followed without delay, for these lights and inspirations from God are transient, not permanent, and therefore the divine call should be obeyed instantly. As of old, when He worked His miracles and went about doing good, “Jesus of Nazareth passeth by”; if we do not take advantage of His passing, He may never return. “I stand at the door and knock,” He said, “If any man shall hear My voice and open to Me, I will come in to him,” if not, that call may never come again.

“Make haste, I beseech you,” exclaims St. Jerome [Letter 53 to St. Paulinus, 11.], “and rather cut than loosen the rope by which your bark is bound fast to the land,” for even a day’s delay deprives a person of invaluable merit, which he would acquire in religion.

Delay is dangerous, and long deliberation, as Msgr. Malou assures us, is unnecessary: “Of all the state of life the religious state is, without contradiction, that which demands the least deliberation, and is that of which the choice should cause less doubt, and provoke the least hesitation; for it is in this state that fewer difficulties are met with, and the best means are found for saving our souls.”

2. "Life in married state and in a state of religious order or in priesthood are equally good ways to sainthood, you just need to discern which one of these God wants you to take."

Your first clause is Jovinian's heresy, against which St. Jerome (Against Jovinian bk. 1) et al. wrote and the Council of Trent, session 24 canon 10 infallibly condemned:

Canon X.—If any one saith, that the marriage state is to be placed above the state of virginity, or of celibacy, and that it is not better and more blessed to remain in virginity, or in celibacy, than to be united in matrimony: let him be anathema.

That virginity/celibacy is a superior means to sanctification than matrimony does not mean that all virgins/celibates necessarily have more merit than marrieds, because sanctity is due to one's degree of charity. Discussing "Whether virginity is more excellent than marriage?" (Summa Theologica II-II q. 152 a. 4), St. Thomas Aquinas writes (ad 2):

Though virginity is better than conjugal continence, a married person may be better than a virgin for two reasons. First, on the part of chastity itself; if to wit, the married person is more prepared in mind to observe virginity, if it should be expedient, than the one who is actually a virgin. Hence Augustine (De Bono Conjug. xxii) charges the virgin to say: "I am no better than Abraham, although the chastity of celibacy is better than the chastity of marriage." Further on he gives the reason for this: "For what I do now, he would have done better, if it were fitting for him to do it then; and what they did I would even do now if it behooved me now to do it." Secondly, because perhaps the person who is not a virgin has some more excellent virtue. Wherefore Augustine says (De Virgin. xliv): "Whence does a virgin know the things that belong to the Lord, however solicitous she be about them, if perchance on account of some mental fault she be not yet ripe for martyrdom, whereas this woman to whom she delighted in preferring herself is already able to drink the chalice of the Lord?"

3. "One can know God's will for his particular state of life via prayer and whether he feels peace (or something like that) when he prays or somewhere else."

See Thomist Fr. Richard Butler, O.P.'s 1960 Religious Vocation: An Unnecessary Mystery.

He would agree with your statement that "One can not know God's will [perfectly] directly and with [perfect] certainty about one's particular state of life," because we cannot know God's essence perfectly (His essence and will are identical, because He is supremely simple). But we do know His will is our sanctification (1 Thess. 4:3: "this is the will of God, your sanctification").

4. "Calling to religious vocation typically involves some kind of event where God is manifest or some deep experience of God."

Pope Pius XII's apostolic constitution Sede Sapientiæ on vocations to the religious life says (part II.) two necessary conditions must be met when discerning a vocation: that one is called by God and called by the Church. For example, canonical impediments to entering religious life would be a clear sign God does not call one to religious life.

See also Pius XII's 1954 encyclical Sacra Virginitas, which refutes many modern errors regarding the religious life and virginity. See also Joseph Marie Perrin, O.P.'s Virginity (esp. ch. 9, "The Gift of a Vocation"), the appendix of which is that encyclical.