Character 瞓: where did the pronunciations come from?
How was it pronounced in older times (i.e. Middle Chinese)?
  


I haven't found a record of 瞓 in classical Chinese, but since 瞓 and 训 are both read as fan in Cantonese, I'll take 训 instead. It is read qhuns in reconstructed Old Chinese that is before the 1st century B.C.  In Middle Chinese it is pronounced as hyonh.


  
  How did the pronunciations come into being?
  


If you mean 瞓, it is obvious that it's created after 训 as a phono-semantic character or 形声字. the x in Mandarin xun comes from qh, then to hy, then to x. The f in Cantonese fan might have come into being along the qh -&gt; hy -&gt; h -&gt; f route. 


  
  Which is the correct Mandarin sound?
  


瞓 isn't a Mandarin word. The dictionaries say it's fèn and it comes from Hokkien or Cantonese. fèn is an approximation of the sound in the dialects. 


  
  If there are more, how did they come into being? Were there semantic loans at any point?
  


If you mean more of "dialectic words" that don't exist in Mandarin such as 瞓, there are quite a few. They exist because there are no counterparts in Mandarin or rather classical Chinese, so people have to make new characters for these words. I don't think semantic loan happened here, but it does involve borrowing existing characters to make new ones.


  
  Could xùn be a misspelling of kùn?
  


It's not misspelling. See answers to question #1 and #2. k to x shift is possible. Similar is the case in western languages where the hard c (read k) shifts to a soft c which sounds similar to the Chinese x.


  
  Could mén, mèn be distortions of fèn?
  


Not impossible: m -&gt; w -&gt; v -&gt; f, For example, in Chinese we have 没(m) 无(w) 否(f) all mean no. But regarding to your question, we need to know who uses the sound men and when it is used. In most online Chinese dictionaries 瞓 is pronounced as fèn, I didn't found any references to men.