Butterflies
We cannot wrap up the Fae without talking about the butterflies. If the bioluminescent moths are the magical stuff of the Mael, then their butterfly cousins should be redolent of light magic. What might happen if one of Felurians butterflies made it through the door stones into mortal? How about the same question with one of cthaeh's!
I cannot conceive how or why the butterflies are important, but observation tells us they clearly are.
Colour is how we divide them and by comparing colours to subjects it appears that there is some method to the madness. Chaos theory.
I think that there is a link between the Cthaehs butterflies and his next words as there seems to be a ceremony taking place during Kvothes encounter with the sacrificial butterfly being chosen by it's colour to answer questions on a specific subject. Each colour pertains to a different field of inquiry. The red one at the start is Kvothe himself and so by dissecting it, Cthaeh can see ten feet through him which is five feet per wing.
The middle section is a knot of two subjects, the Chandrian and the Amyr. The butterflies involved here are all shared between blue and purple.
The Three green ones at the end coincide with an abrupt change of topic as Cthaeh steers the questions onto Denna.
Other coloured insects are available and we can suspect they represent other rradily available subjects, but they weren't eaten in this specific encounter and Kvothe fled with the line 'I have so much more to tell you' ringing in his ears.
If you can accept that as plausible theory then you have your answer already but there is still the question of separating the blues and purples into the Amyr and the 7, and that's quite a tricky puzzle.
Red offends his aesthetic . A mortal in Fae naturally offends him suggesting the red one represents Kvothe himself.
Blue/Black slightly sweet? Which is something to chew on but this shade of blue colour is not to be confused with the different blue that he labels sapphire. My best guess on the sapphire subject would be Felurian since her name is mentioned at this juncture.
So by now the Cthaeh has 'read up' on three different characters. Kvothe, unknown, and Felurian.
With this information fresh to hand it steers the conversation towards Kvothe picking a subject close to his heart, and knowing what it now knows, confidently predicts that Kvothe will ask it about the Chandrian since that is his number one desire and so breaks two more blues in preparation. But Kvothe doesn't ask about the Chandrian, instead he asks about the Amyr. This response was Not what the omnipotent oracle had just prepared for, Amyr are then a different colour to Chandrian meaning tgat it has made a mistake by eating the wrong butterfly. You might scoff here and say that that cannot be since Cthaeh is infallible, but this clearly not so, if nothing had gone wrong then the Cthaeh would remain in calm control, but instead it displays its anger with 'Kyxxs' a word clearly born of anger and curses. Kvothe has just out- bargained the Cthaeh.
This implies that tte blue/black butterfly answer for which it has prepared is actually the colour of the 7 , and Cthaeh thinks of them as being slightly sweet.
In order to research questions about the Amyr, it needs to consume some purple butterflies and the rest of this middle phase is supported by a mixture of both colours. When Kvothe asks why the purple (Amyr) butterflies the Cthaeh replied 'pure spite' and that it was envious of their carefree innocence. This must then be a hint regarding its opinion of the subject of the Order Amyr.
Then comes quite a long passage on Cinder alone, whose butterfly was then likely as not the very first blue/black one that Cthaeh had pre-selected before kvothe tripped him up with the Amyr question. Finally the Cthaeh shifts the conversation onto a new topic and everything else merges into the final three green butterflies of Denna and/or her patron who's future may or may not still be connected to the blue/black taste of Cinder, I'll leave that for you to decide.