Here are some more thoughts on the subject. Note that they are what I think, and so are not to be taken as authoritative.
7.1. IF and WHETHER
I don't know if/whether Mila is coming tomorrow (or not).
I am going out if Mila is coming.
I am going out whether Mila is coming or not.
At first sight there is little difference in meaning in  whether we use IF or WHETHER, though only with the latter does or not have an acceptable alternative position immediately preceding Mila. In , however, WHETHER cannot be used, and in  most native speakers would find IF unusual. There is clearly, therefore, a difference in meaning between the two words.
With IF we are considering the uncertainty of a happening or state. This means that we are not certain of its actual happening or state: its non-happening or non-state is a possibility, but that negative situation is not explicitly (or implicitly) considered. Indeed, the negative situation may change the meaning of the utterance as a whole. In , the speaker states only that in the event of Mila's coming, he is going out. The implication that in the event of Mila's not-coming the speaker will not go out may be intended by the speaker, or such an inference may be drawn by the listener, but it is impossible to say for sure. We have a double uncertainty: about the happening or state in the IF-clause, and about the consequence stated in the other clause in the event of non-happening or non-state.
With WHETHER, on the other hand, the negative situation is always implicitly (and often explicitly) stated, and may change the meaning of the utterance as a whole. In  there is certainty that the speaker is going out. The singleuncertainty is about the happening or state in the WHETHER-clause. The two utterances are fundamentally different in meaning, a necessity highlighted by the need to add or not to the WHETHER-clause  and the need not to add it to the IF-clause .
 presents a different situation. Here, there is still the same uncertainty about whether Mila is coming. However if the speaker does not know about her coming, then he clearly does not know about her not-coming. Knowing is not a consequence of coming, as opposed to going out in , which is a consequence of coming. Thus, while the difference in meaning between IF and WHETHER is the same as ever, the differences in the practical results of the difference in meanings are minimal. This explains why we can use either word in such non-consequential statements, and also why if not is acceptable (or omissible) with both words.