Things like use of the nominative case and nominative form of the verb "to be" in instances where uncertainty of expression called for the subjunctive. Example: "I would not do that if I were he."

I don't think you're remembering that quite correctly, or you're misusing terms, or something. There are actually two grammar trip-ups in ``I would not do that if I were he.'', which is correct English, but not, I think, quite for the reasons you state.

The first, and simpler one, is that the verb to be (in the form ``were'' in this sentence) is an intransitive verb, which means that it does not take a direct object. As such, when you use a noun or pronoun in the predicate side of the sentence, it is being used as a predicate nominative, which means that it's renaming the subject. As should be obvious, the direct object would be in the objective case, and the predicate nominative in nominative case. In English, nouns do not take different forms between nominative (or subjective) and objective cases, but pronouns often do, and ``he'' is the nominative case of the pronoun that would be ``him'' in objective case. A good, simple example is that one should not state on the phone ``It's me'', but, rather, ``It is I'', à la Lamont Cranston.

The second has to do with the subjunctive mood or tense. The subjunctive mood is used when, as you say, the state is uncertain, like when you use ``if'' or ``might''. In modern English, the subjunctive forms of the vast majority of verbs, if not all of them, are the same as their third-person past tense forms. Many modern English language scholars will tell you that the subjunctive form is all but dead. It really has no reason to still be here, as there is always some other word that indicates the subjunctivity of the verb. I think that it still sounds nicer to use the subjunctive, though.

Anyway, my point is that those two rules are not related, so you're either conflating those two things, or your teacher taught you rules combined together for common happenstances.