Some indications for the special layouts:
Shadow emblem
Big swirl
I don't have specific patterns for the big swirl, I just go up and down until I can get rid of the extra tiles in the corners. It might take several up-and-downs, and if I get tiles in the corners (where it's pretty hard to make it disappear before going into the pointy end) I sometimes switch colors. Whatever works, really. This is the difficult one, so I recommend starting with this one if you think you might reset at some point.
Little swirl
The key for this one is to go towards either of the point ends, until either you get rid of everything, or there's only one tile left. I find it a bit easier to try and bring my last tile to the end at the center of the spiral.
Once you have that, start from the other end. Depending on whether you start by converting 3 or 4 tiles (or 2 or 3 if you start from the center of the spiral), making sure to cover the whole swirl and not switching twice the same tile, you should be able to either turn the entire swirl the opposite color, or turn all the tile
except the last one. Which is what you want to do if you have just the one tile left.
Make sure the inside swirl is the same color as the outside one, and you're done!
Four hexagons
There's nothing tricky about this one. Solve the two medium sized hexagons. If they're of different colors, randomly click one of them to change its tiles, and solve it again. Make sure you start by trying to eliminate the tiles of
the opposite color of the other hexagon. Most strategies lead to a change of dominant color in the solving phase.
For the little hexagons, just randomly click until you understand how they work. They're really pretty simple.
Light emblem
The light emblem is my favorite special layout. It can be really fast, and it's very straightforwards.
I'll describe the strategies, going from the left to the right.
A general approach to this layout is to try and bring any leftover tile to the top of the "rays of light". I give approaches to solve each ray when there's only one tile left. If you didn't have to go through this phase, you have been dealt a lucky starting point, and it's all good too ^^
For the first ray of light, the mechanism to get rid of the last tile is pretty much the same as the small swirl of the shadow emblem. Start by converting the five bottom tiles (picture coming later). Then convert the four tiles left, and you're good.
If you want to switch the color of this ray, start with the bottom tile to convert three tiles, then convert the top two tiles by clicking on the top-most tile. You're left with a cluster you can eliminate in one click.
For the second ray, the process to change colors is complicated, and is a bit useless unless you really want to make [insert your favorite] win. I generally solve this one, then align the other colors on this ray.
To change all but the top-most tile, there's a series of tiles to click. See the pictures. The main idea is to go downwards, and then climb up, having done a little loop at the point to switch the color. (Apologies for the different sizes, I didn't crop them automatically)
The third and fourth rays are also pretty straightforwards to solve. I'll come back and edit in details later, once I have some pictures done. :)
I hope someone will find this useful :D