I am curious. Our Bishop is a Jesuit. What is his relationship to his Superior? Is he still under his Superior or does he now answer directly to the Pope?
I also know that the Jesuits serve the Pope, but what about other Orders?
Allow me a brief moment of pedantry here (!) : the Jesuits are not a religious order, but an institute of clerks regular (or canons regular - the meaning is the same). Although many of us refer to all religious as belonging to an ‘order’ this is not technically correct: the generic term that should be used is ‘religious institute’, which includes orders, congregations and other forms of religious life.
The reason I make the point - other than because I am a shameless pedant - is because you are, of course, asking a question of canon law, and canon law does distingush between different types of religious institutes in terms of their rights and obligations.
The relevant canons to your question are nn. 705-707, which I’ll quote in full.
*Can. 705 A religious raised to the episcopate remains a member of his institute but is subject only to the Roman Pontiff by virtue of the vow of obedience and is not bound by obligations which he himself prudently judges cannot be reconciled with his condition.
Can. 706 The religious mentioned above:
1/ if he has lost the right of ownership of goods through profession, has the use, revenue, and administration of goods which accrue to him; a diocesan bishop and the others mentioned in can. 381, §2, however, acquire property on behalf of the particular church; others, on behalf of the institute or the Holy See insofar as the institute is capable or not of possession;
2/ if he has not lost the right of ownership of goods through profession, recovers the use, revenue, and administration of the goods which he had; those things which accrue to him afterwards he fully acquires for himself;
3/ in either case, however, must dispose of goods according to the intention of the donors when they do not accrue to him personally.
Can. 707 §1. A retired religious bishop can choose a place of residence even outside the houses of his institute, unless the Apostolic See has provided otherwise.
§2. If he has served some diocese, can. 402, §2 is to be observed with respect to his appropriate and worthy support, unless his own institute wishes to provide such support; otherwise the Apostolic See is to provide in another manner.
*
Fundamentally, the upshot of these provisions is that the bishop’s religious vows can only continue to be applied where this does not interfere with his episcopal state, and in terms of obedience this means that the authority of his superior is suspended, and poverty mitigated as appropriate to his episcopal duties. Upon retirement, the bishop can choose to continue to live a diocesan rather than religious existence.
This is sometimes described as the religious having their vows ‘suspended’ upon being raised to the episcopacy, but that is not really correct. Although his vow of obedience to superiors is not enforced, he is nevertheless obliged to consider other aspects of his vows and the religious charism that he follows, and apply them wherever they do not interfere with his new responsibilities. Whilst that makes the application of the vows into largely a matter of his own judgment, it does not give him complete freedom from them.
One other proviso: a definitive judgment of the Holy See in 1986 declared that a religious bishop could neither vote nor stand for office in his own religious institute.
Hope this helps.