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Jesus, Who knows everything already, had no need to ask questions except to teach us.

I agree.

My interpretation is that He asked the doctors questions to test them and to confuse them.

And then, He took the discussion further and solved the doubts that He had raised by his questioning. He was the master, even though He was just twelve years old.

This method happens with some frequency in the Gospels. A good example is when Our Lord asked a certain disciple (Philip, I think), just before the miracle of mutiplying bread, how they would feed all those people. If I remember correctly, the text says explicitly that He did this to test Philip, and not because He didn't know what to do, which would be absurd.

St. John the Baptist also instructs his own disciples to ask if Jesus is really the messiah. It is obvious that he had no doubt about this, but he acted like this to make his disciples believe that Our Lord was really the messiah.

To answer the question, as a general rule, yes. Individual priests privately differ, and some chapels will adopt more-or-less generous policies towards the matter, but the short answer remains yes, and this is reinforced by those priests who have consistently been in the most prominent positions of education for the SSPX.

I refer to one of my previous posts that rebuts a number of the problems in most SSPX thinking regarding this issue: https://www.cathinfo.com/sspx-resistance-news/sspx-letter-on-the-vaxing-of-nz-teachers/msg799255/#msg799255

There is an deep lack of understanding of Catholic philosophy of education even to the very top of the current SSPX hierarchy. I know a certain SSPX superintendent who has revealed an appalling attitude towards homeschooling and such parents behind closed doors.

This is of course not to say there are problems with some homeschooling circuмstances. But the other side of that same argument is, are there no problems to schools? Every solution is a compromise to some degree. Families are imperfect societies; hence the Church teaches that schools supplement family education, but must not replace it. But schools, too, are imperfect in many ways. If a child learns the ways of the world from his school peers, or even worse from his teacher, is corrupted in vice, or Heaven forbid, is involved in an abusive situation, what good was the school? If worse, those in charge of the school have repeatedly neglected their grave responsibilities to ensure a safe, holy environment and enforce the highest standards of virtue and behavior among the children, isn't "traditional Catholic academy" under the "SSPX" all a tragic marketing joke?

Once the corruption begins, at such an impressionable age, it is extremely hard to undo. The Jesuits had the old saying, "Give me a child until he is 7, and I will show you the man he will be come." This isn't to be understood in a mechanistic, input-output manner, but that as anyone who has experience teaching young children and seeing their progress in the later years knows full well, the seeds and foundation are all clearly visible at a very young age. It takes much moral effort, much grace, and much sorrow to correct a faulty foundation in the later years.