How is masculinity and manhood represented by each character by three levels of masculinity (class, universal, race)?

The three male characters of the play are, of course, Dr. Rank, Krogstad, and Torvald, whom I'll try to deal with individually and in comparison to one another. First, however, I would disagree somewhat that masculinity can necessarily be broken down into the three elements you've specified without a huge amount of overlap, to say the least. With regard to the class factor, all the characters in Ibsen's play would probably be characterized as upper middle-class. The requirements of this class seem chiefly to be the proverbial "good provider." Torvald fulfills this function. Dr. Rank does not even seem to have a family, and Krogstad is a failure for the most part in this regard. But Torvald is at the same time basically a hypocrite and a fool. The race-based feature of masculinity, in my view, is the least significant in Ibsen, unless we are to assign some special trait Northern European men are expected to have. Would this, perhaps, be that they are more expected to keep their outward emotions in check than other men? If so, I would regard this as a stereotype not borne out in the play at all, except in Dr. Rank. His stoicism in the face of both illness and his hopeless love for Nora are evident. The other two men, Krogstad and Torvald are, by comparison, whiners, to put it colloquially. Krogstad is a self-pitying and deceptive man who comes off the weakest by any standard of masculinity. Through the first part of the story Torvald appears a decent man (apart from his demeaning way of addressing Nora as his "little bird," and so on) but his weaknesses and irrational domineering increase in equal proportion as the action advances, probably because the two qualities are interrelated. His vicious outburst at Nora when he is made aware of the blackmail plot shows him a coward. This has to be the worst violation of the universal "male code" (if such a thing exists) that's exhibited by any of the men. Torvald is terrified at losing his own status and wealth, and his reaction is to blame Nora for everything, though the loan taken out fraudulently by her was actually done for his benefit.
What seems to contradict both this failure of Torvald by any normal standards, and the stereotypical ideal of masculine dominance, is Torvald's plea, when Nora finally makes ready to leave him, that she stay and the two of them live together platonically. She, of course, doesn't believe him and remarks that "we both know how long that would last." But it is an interesting point that Torvald now seems to express what is the genuinely masculine (as well as feminine) need for simple companionship. This is the most universal quality that all the men in the play, regardless of their faults, end up expressing, though, as stated, there is nothing about it that relates specifically to "masculinity" on any level.