All typed characters are Unicode APPROXIMATIONS. Where two characters are given, the first is lowercase and the second uppercase. See capitalisation. This alphabet is indeed ordered. (In case you're wondering, the consonants are roughly ordered from the front of the mouth to the back.)

Látunc is the latinised alphabet: it's a protocol allowing you to write Ayunc using a standard English keyboard (using the AltGr key for á). So "Ayunc" in Látunc would be written as Áyunc. The name for each letter has been transcribed into Látunc as an example. Látunc is mostly intuitive to native English speakers, with the exception of "a" indicating /ʌ/, which many associate with "u". For simplicity and distinction, multi-character Látunc transcriptions to a single Ayunc character are surrounded by round brackets (so that an "s" followed by an "h" can be distinguished from a "(sh)"). These brackets can be implied where it doesn't cause ambiguity of vocabulary. Don't ask why "Látunc" gets an accent in English but "Áyunc" doesn't.

You may notice that this is quite a small phonology. Thus, there are some diacritics in Ayunc for a more complete alphabet. First and foremost is the bar (to be renamed at a later date): this is not unlike a macron, sitting on top of select letters. When multiple barred letters are next to each other, the bar is drawn as a single line over all letters (which can't be elegantly achieved in Unicode, for the time being).
In general, this diacritic has the effect of turning a voiced consonant into its voiceless counterpart, with two exceptions: it turns ipa into yipa (which functions similarly to a German j or an English y), and on top of a capital Ipa, it is drawn more like a breve embedded inside the letter; it turns hiza, the glottal approximant, into khiza, which may be pronounced in a variety of manners depending on accent and the ease within the context of the word but is usually an uvula or palatal fricative or similar (both consonants are voiceless). Instead of being carried over to Látunc, each "softened" letter has its own Látunc parallel.
The other diacritic is a grave accent (`) which is occasionally placed above vowels to indicate major or minor stress within a word. For simplicity, it will not be included in the table below as it's simple to understand and rarely found (mostly in dictionaries, for example). This diacritic is never carried over onto Látunc, for the primary reason that it's not present on most keyboards (and also to avoid confusion with á).
With the addition of these diacritics, the Ayunc phonology is not dissimilar from English or German.

Using these characters, some digraphs and multi-character phonemes follow quite logically, including some diphthongs, although they're not common in standard Ayunc and mostly for loanwords or transliterations of English. Látunc transcriptions aren't given because they're what you'd expect them to be.