Unfortunately, learning names - such as subjunctive - does not necessarily constitute knowledge (on this see the humorous interview of Richard Feynman on the name of birds).
A difficulty of English grammar
What makes English grammar sometimes difficult to understand, especially for native speakers, is that it has very few inflections. Whereas in other languages (French, Italian), you would have different forms for infinitive, subjunctive, etc., in English the same "atom" has to be repurposed for many uses.
This economy of means is a truly remarkable feature of the English language and it might be a factor in the ease with which foreigners can learn it. On the other hand, that could also be a drawback in some cases.
For example eat in English could translate (among others) into French as:
- manger (infinitive)
- mange (1st/3rd person singular or imperative)
- manges (2st person singular)
In those more inflected languages, grammar is often easier to learn, because it may be sufficient to look at the word itself to understand its function. And since categorizing things by shape rather than meaning is far easier, grammar may appear clearer on that account. In a language such as English, people are more liable to get confused when the same form is used to mean different things (polysemy).
Back to your question, we are dealing with two distinct phenomena:
Infinitive used as imperative, third person
God bless you.
It is required that the applicant be 18 years old and possess a valid driver's license.
What you were taught is a mandative subjunctive, in reality conveys an idea of imperative of the 3rd person (which could be said existed in Latin: caveat emptor: the buyer must beware; but it was also the form of the subjunctive). Since most Western languages of the Middle Ages are sadly missing this useful form, they had to resort the same gimmick: so they used prevalently the subjunctive form to convey that idea.
Que Dieu vous bénisse.
Nous exigeons que le candidat ait 18 ans.
Since (modern) English did not have even that tense (formally), it fell back to infinitive. Now, why English grammarians called their repurposed infinitive a subjunctive, instead of an imperative is (my guess) because they wanted to align their terminology on French, which used to be the aristocratic language under the Anglo-Norman monarchy and then remained a language of culture.
While the solution of the grammarians may have been handy, we could argue they could have carried their reasoning to its logical conclusion. Regardless of how we conventionally call this bird (there would not be a sufficient case to abolish the term subjunctive), it is semantically an imperative.
Simple past used as a hypothetical condition
If I were you, which we both are thankful I am not, I wouldn't do that.
In that case, it seems a calque (loan) from French:
Si j'étais vous (...)
... which was the imperfect (and not the French simple past), which kind of makes sense: the condition is not realized.
Unfortunately, the simple past in English is also used to convey the imperfect when needed. In this case again, a simple linguistic device was thrown into the big cauldron of polysemy. The problem is that the meaning of "if I were you", is easily understandable intuitively, but to explain why it takes this form becomes difficult, unless one already has notions of other languages.
Back to your "if I were", this pretended subjunctive is actually used to build a conditional sentence, which would be, in French:
Si j'étais vous, je ne ferais pas cela.
Again, English is lacking the inflections necessary for the conditional, which is why the auxiliary form would (invariable) is used. Hence:
If I were you, I would not do that.
As for:
I dreamed I were a fireman.
It is a simple past form ("I were" used to be common, before it became obsolete). While it has gone out of usage for most cases, it has remained acceptable for expressing unreal situations -- likely by analogy with the previous case, or perhaps a kind of attraction -- and it is conventionally called subjunctive. Actually, one would easily use the modern form and (at the cost of losing an almost imperceptible nuance) it might communicate the idea just as well:
I dreamed I was a fireman.
