Great question, Sergey!
You should learn them all, however, you're correct that the 3rd conditional is often modified in speaking -- for example, the correct form "If I had known, I wouldn't have done it" will often be "If I knew, I wouldn't have done it."
There are also mixed conditionals, where the cause and effect are in different times, for example "If I had studied medicine (past unreal), I would be a doctor (present imaginary)." Note that with mixed conditionals, the cause always takes place at an earlier time than the effect... this is not a grammar rule, so much as a physical law of the universe :)
Type 1: Future real possibility.
Type 2: Present (or sort of future) alternate reality -- not true, but could be achieved by magic.
Type 3: Past unreal (contrary to fact). Only possible if you have magic powers and time travel abilities as well.
As far as the "zero conditional," an example would be, "If he watches TV at night he falls asleep." This is a present real "conditional." You could just as easily use "when" with the zero conditional, with no change in meaning. You can use "when" in the 1st conditional, but the meaning is different.
Really, the formation of the conditionals is a lot easier than knowing when to use them. As far as your terminology, I like it, except I think the phrase "conditional perfect" is clearer in this context than "future in the past."