Consonants as source of vowels

Hi!

For my polysynthetic conlang Qthen|gai, I will need to do the next
evolution step sometime: to work out a nice set of highly complicated
fusion rules for the morpheme strings.  Currently, only grammar
and phonemes are hard to learn.  This has to be changed. :-))

In order to achieve part of this, I thought that for each of the three
interesting vowels, /a, i, u/ and possibly for /@/, too, I should find
one or two corresponding consonants for each one.  In certain
phonological contexts, the vowel will appear, on others, the
consonant, and yet in others, the consonant will generate interesting
mutations in clusters.  That's the basic idea.  One thought is to
split the current diphthongs /ai/, /ui/, /au/ and /ua/ (all falling)
so that one group has a phonemic vowel at the end, while the other has
a phonemic consonant.

An obvious vowel-consonant correspondance might be something like:

   /i/ ~ /j/
   /u/ ~ /w/
   /a/ ~ /?\/

But I don't know what interesting effects this might produce, since
the vowels are too similar to the corresponding consonant.

Now, a more interesting correspondence seems to occur in some frequent
mutations, like in French, where e.g. |ct| -> |it| (as in |fait| <
|factum|).  This also happened in Portuguese (|leitor| < |lector|).

I might, therefore, use
   /i/ ~ /k/

And I could also have
   /u/ ~ /k/
as in Portuguese |doutor| < |doctor|.

Such correspondences could make quite interesting mutations possible.

Question 1: I don't fully understand the motivation for such a shift.
Why and how does /k/ shift to /i/ or /u/?

Question 2: What other vowel-consonant pairs are feasible in such a
way?  I'm searching for any not-so-common and interesting
correspondence of a vowel and a consonant.  E.g., as here, in shifts.
Example: (Pre-)Ancient Greek's shift /a/ < /n=/.

Question 3: Something related but different: is there a good overview
of Korean phonological rules somewhere on the net?

Question 4: More generally: what interesting phonological phenomena
have you seen in languages?

Bye,
  Henrik

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