Thanks for the questions. I have omitted the questions on a particular priest and diocese for the moment. I believe the case you raise is significant and I will try to answer your questions, but I wanted to go with these more general questions first. It is always tragic when there is a disedifying use of (or refusal to use) c 603 by bishops who really may not understand either the canon, its history, or solitary eremitical life itself, particularly when they use it to shoehorn someone into this vocational option despite their manifest lack of suitability, preparation, and discernment, but it does happen. So, let me answer the above questions first, at least until I have done what I can to ascertain the facts in the specific case you raised. Some of these repeat responses I have given others in the past so be sure and check past posts as well.
It is not common for dioceses to profess secular priests, especially younger ones, under canon 603. There are several reasons. First, during seminary training a significant program of pastoral work and discernment is undertaken. By the time one reaches the point of readiness for ordination everyone is pretty clear that the young man is called to an active apostolate whether or not he has a contemplative bent or not. in light of this there must be really significant signs of a different vocation to change the young priest's heart and mind on the matter and those of his bishop, et al; this will take a similarly significant time to reveal itself and even then all kinds of steps will be taken to help ease the young priest's dis-ease with his parish assignments.
After all the time, energy, and expense, spent in the original discernment and formation processes no prudent bishop or priest is going to jump (or allow a priest to jump) into life as a hermit, much less profession and consecration under c 603, nor should the Office of Consecrated Life allow a precipitous move from active priestly ministry to consecrated eremitical life. It is not fair to anyone involved in such a case, nor is it an appropriate use of the canon. Moreover, it is offensive to dioceses and diocesan hermits who have spent the requisite time and energy in truly discerning hundreds of such vocations since the canon was published in 1983 --- just as it is unjust and offensive to those who petitioned in good faith for admission to profession and consecration and, for whatever good reasons, were eventually refused.
Generally speaking, then, yes, a priest candidate will undergo the same formation and discernment process as anyone else in preparation for admission to a life of the evangelical counsels lived in the silence of solitude. After all, as I have pointed out a number of times over the years, this is a uniquely significant and rare vocation, and very few, relatively speaking, are called to human wholeness and holiness in such a vocation. It deserves care and attentiveness by all concerned. Secular priests with promises of obedience to their bishops will need to prepare for a vow of religious obedience to God in the hands of their bishops and anyone the bishop delegates to serve in this way. Similarly c 603 requires profession of the Evangelical Counsels including religious poverty and chastity in celibacy. In my understanding of these vows they are richer, grounded differently in different realities, and thus require a different preparation than do, for instance, the commitment to the discipline of celibacy or a life given over to some form of "simplicity".
If you are asking whether a vow of religious poverty could simply be added to the commitments of celibacy and obedience made by secular (diocesan) priests, my sense is no, canon 603 and the Rite of Religious Profession used for Canon 603 professions require public vows (or other sacred bonds) made to God of the Evangelical Counsels. These are not identical to the commitments (promises) made by secular priests to their bishops. Remember that the three evangelical counsels together make up the lion's share of an organic profession or self-gift to God; they must be similarly grounded in a love which demands that God and God's Kingdom be primary in matters of wealth, relationships, and power (thus, religious poverty, chastity in celibacy, and religious obedience). Also, it is important to remember that profession itself is a broader act than the making of vows, as central as vows may be to the act of profession. This means that one does not reduce it to the making of vows and certainly not to an act in which one adds a single vow to other varying commitments; profession is an exhaustive and ecclesial act of self-gift which, when definitive (or perpetual), will also include God's consecration of the person.
You ask what I would be looking for as I assessed a priest candidate for c 603 consecration. In light of what I have already said, I would be looking for a contemplative who had been successful in his active ministry as a parish priest but who had developed as a contemplative over a period of years. I would look for someone who, again for a period of years (at least 7-10), had developed a life given over to substantial silence and solitude and who had discovered an undeniable call to eremitical life rooted at every point in the charism of what c 603 calls "the silence of solitude".
I would look for a priest who had worked with a spiritual director regularly and over a period of years to develop a life of prayer nourished in this context and always calling him back to it in ways which led everyone who knew him to recognize a potential hermit -- not because he could not live his priestly vocation and active ministry, but because these things had absolutely required what is for him this form of deeper love and were ultimately fulfilled and perhaps transcended in it. (For any hermit engaged in limited ministry I would always look for the ministry to be rooted in the silence of solitude and lead the hermit back to it in an integral way; the silence of solitude always needs to be primary and the lifestyle contemplative. A "hermitage" is not merely a base of operations from which to launch an essentially active lifestyle, nor is it to be used as a way of controlling (or appeasing) problematical priests who simply "don't fit" in parish ministry or the diocesan culture.
Despite, or maybe precisely because a hermit's life is characterized by its "stricter separation from the world" (which does not merely refer to the world outside the hermitage per se), hermitages are not escapist; they are a paradoxical and profoundly loving way of engaging in and on behalf of the life of the diocese and parish. I would argue that priests who may ultimately discern with the church that they are being called to life under c 603 must demonstrate a long history of loving both parish and diocesan life while struggling to love it more deeply from a contemplative perspective.
Thus, I would look for a priest whose greatest success in his vocation to a priestly apostolate was the evolution of his love of God, self, and others into the solitude of authentic eremitical life, not into some ideological excuse or individualistic isolation. After all, his very life in the silence of solitude must itself be a prayer; it must itself be a ministry --- indeed, the hermit's primary ministry and the ground and source of any other limited ministry. It must be a witness to all but especially to the marginalized left isolated by life's circumstances that such life can be redeemed by God's love and transformed into the wholeness, personal quies, and communion hermits know as "the silence of solitude". It ordinarily takes careful and long discernment and formation to be sure enough of such a vocation to admit one to consecration under c 603; for priests already publicly called and ordained to an active apostolate at least as great care should be taken as for any other candidate for consecration.