Solutions

[michael_kuerbis]

The game provides the solutions to its puzzles. Well, not directly, you have to poke around in the game files a little. I will refer to Windows from now on, but it should be possible under OS X as well.
Open the KAMI's game folder. Open the subfolder "puzzles". StageA - StageE refer to the classic levels, 5Col is the first section of the premium levels, StagePat1 is the second one. [update] The third section is Convolution. [/update]
Now these folders contain XML files describing the levels and their solutions. These XML files can be opened with a text editor, a web browser, or an XML editor if you are fancy.
Each level file contains a section (tag in XML-speak) labelled solution, these have subsections labelled turn. Ignore the value of length, sometimes it's incorrect, but it doesn't matter.
Now each turn section describes the turn. The values x and y refer to the coordinates on the grid. The coordinate system starts in the upper left corner and with the field (0,0). That obviously means that the uppermost line is line 0 and the leftest column is column 0.
Colour refers to the colour to use in the turn. However, the numbering of the colours starts with 0 instead of 1, refers to the colour choice bar at the bottom of the grid and goes from left to right.

Equipped with this information it should be relatively easy to create a visual walkthrough based on screenshots. It would be nice if somebody were to make one since the integrated solutions are a bit fiddly to use.

[Abalone]

Ah, thx for this information.
Since I got stuck at one level and couldn't find any videos on youtube (i myself prefer to watch videos instead of reading articles with screenshots) I just started my own channel two days ago and posted solutions for all levels available 'til now.
http://www.youtube.com/user/mespetitsjoujoux/videos (there's also a playlist for KAMI)

[Khul]

I got stuck on the last 2 puzzles in classic mode. Even thought about making vids for the solutions a few weeks ago when I couldn't find any. You beat me to it :p