As Wang Dingwei notes in his answer, 瞓 is a phono-semantic character that uses 訓 (also pronounced
fan3 in Cantonese) as the phonetic component to represent the word
fan3 in its meaning of "sleep". However, 瞓 is a character that was invented in recent times. The phonetic 訓 was chosen because it happens to have the same pronunciation in modern Cantonese, but that does not mean that the historical phonological analysis of 瞓 should be the same as 訓.
Your CantoDict source mentions that the origin of the word is actually 困, and this is indeed the correct origin. 《康熙字典》 mentions that "tired and weary" is among its definitions:
The character 睏 was sometimes used in order differentiate it from the other meanings of 困. The modern Cantonese pronunciation of 困 is
kwan3 rather than
fan3 though, so how did it end up getting its current pronunciation of
fan3? It turns out that it is the result of regular sound change from Middle Chinese, and in fact it's the
kwan3 reading that is the exception.
Compare the following words, all of which have an
f- initial in modern Cantonese but had a /kʰu-/ initial in Middle Chinese:
- 苦 MC: /kʰuo/ > C:
- 堀 MC: /kʰuet/ > C:
- 快 MC: /kʰuai/ > C:
- 寬闊 MC: /kʰuan kʰuat/ > C:
As an aside, Mandarin retained the MC /kʰu-/ initial (pinyin:
ku-) essentially unaltered (cf.,
kuān kuò, respectively).
困 was pronounced /kʰuən/ in Middle Chinese. 《康熙字典》 mentions that 困 has the fanqie 苦悶切, so by analogy it should have the same initial as 苦 and should be read as
fan3 rather than
kwan3 in modern Cantonese if the sound changes were consistent. However for some reason its literary pronunciation in modern Cantonese happened to preserve the older /kʰu-/ initial.
Given this, the answers to your first three questions should actually be analyzing 困 rather than 訓:
- How was it pronounced in older times (i.e. Middle Chinese)?
As mentioned previously, 困 was pronounced /kʰuən/ in Middle Chinese.
- How did the pronunciations come into being?
f- came from Middle Chinese /kʰu-/. MC /kʰ-/ had at one point become /h-/ somewhere in the course between MC and Cantonese. /h-/ initial words that did not have a /-u-/ medial remained /h-/, for example:
- 開 MC: /kʰai/ > C:
- 看 MC: /kʰan/ > C:
- 可 MC: /kʰa/ > C:
- 客 MC: /kʰɐk/ > C:
- 肯 MC: /kʰəŋ/ > C:
- 口 MC: /kʰəu/ > C:
However, those with the medial (i.e., /hu-/) underwent a further change to become
f- in modern Cantonese, as previously noted.
As an aside, the /kʰ-/ to /h-/ shift is not an unusual sound change. A similar shift happened in the Germanic languages (e.g., compare Latin canis vs. English hound, cor vs. heart, centum vs. hundred, etc.; see Grimm's Law).
- Which is the correct Mandarin sound?
This is simply the pronunciation of 困 in Modern Mandarin, which is
Your remaining three questions are in regards to the character 瞓 itself rather than the actual word that
fan3 was derived from (困). Because it's a character that was invented to represent dialectical pronunciations, it's hard to determine how the other "Mandarin" pronunciations came about without additional references to where they were found, as Wang Dingwei mentioned in his answer.