Consistency was never my strong point.I am sorry if you, 5jj, will say nothing more on this subject. You seem to bring to it considerable expertise.
Yes. The exact figure differs according to which variety we are talking about.I believe that most English speakers use about 42 phonemes.The International Phonetic Alphabet, with its diacritics can be used to represent any and every sound known to exist in languages all over the world - and a few that are not known to exist.I am not sure that any system -- even the IPA -- can adequately represent them.Your dialect has only one phoneme there, and you would use one phonemic symbol. My dialect has separate phonemes, and we use different phonemic symbols for the vowel sound in the two words. I don't know if your 'cot/caught' vowel sound is exactly the same as my 'caught' vowel. If it is, then we would use the same IPA symbol when transcribing your 'cot/caught' vowel and my 'caught' vowel, and a different one for my 'cot' vowel. If, however, it is not exactly the same, then we would use three IPA symbols, one for your 'cot/caught' vowel, one for my 'cot vowel and one for my 'caught' vowel.They seem to be on such a "sliding scale". E.g. "cot" and "caught" in my dialect sound identical -- \kot\.
Retired English Teacher