The most common (and pretty much the only) tests don’t test any specific type of intelligence, since it’s considerably more difficult. For that kind of more in-depth examination you probably need to visit a psychologist, like you did.

As for the test you took itself, I can’t really say too much about it. It might have been personalized for you. So someone with worse access to education may receive an entirely different test. I think this is what should happen, after a reasonably thorough interview.

Hard to say precisely, and this may be beyond the scope of my current knowledge. I took psychology classes and read some books, both of which covered IQ basics in great detail, but didn’t go into specialized tests. What you’re saying is quite interesting, so I may read up on that or ask my psychiatrist.