You confuse "if" you use in conditionals with "if" you use in reported speech. Conditional "if" is a conjunction which creates a condition and has nothing to do with "whether" "if" which you use in reported speech is a particle the same as "whether" and they are interchangeable: "He asked me if/whether I was going to come."

"If" is the more common and most functional of the two words; much more common and versatile than "whether" "If" is correct in your 1st and 3rd sentences: If you punch me, I will punch you back. If you shout me dinner, I will shout you drinks. I don't know if it is true/I don't know if it is true, or not. I don't know if it is true, or just a rumour. "If" is only concerned with one decision, or one yes/no answer. Like the logic in computer systems IF xxx >= 5, do this, IF xxx <=4 do this. "I don't know whether it is true" is correct. I guess there is an implication in the phrase "true or not (true)". See next sentence. "Whether you do this, it will happen" is incorrect. "Whether" is used when there are 2 choices/options. Whether is is true, OR NOT. Whether you do this, OR NOT, then xyz will happen. Whether you join us for the party, or not (join us), we will have a good time. Whether it is sunny or cloudy, we will still be sailing.

e.g. If you do this, it will happen this. (correct) Should be> If you do this, it will happen. Whether you do this, it will happen this. (incorrect) Could be> Whether you do this or not, it might still happen. I don't know if it is true. (incorrect) This is correct. More commonly found with> I don't know if it is true or not. I don't know whether it is true. (correct) Also correct. Your generalisation at start > Is it true that "if" should be used only in if-sentences and "whether" in all the other cases? Does not apply in all cases and as such is not much help. Moreover, both if and whether can be used for each other, but might require changes of sentence to make sense. If is normally used for cause and effect sentences: If I cut your hair, it will look nice. Whereas whether is used where cause and effect and not linked. Whether I cut your hair or not, it will look nice.