In terms of distribution, there are some rather strict restrictions, plus some fairly strong tendencies in the language. The most notable ones are that, mainly as a result of the prevalences of noun and person marking prefixes, the set of permissible word-initial consonants is limited to p, t, ty, s, x, xw, m, n, ny, r, y, w. Furthermore p and xw are restricted to particles (pa‘ "negative", pu "in this manner, like so" and xwe "prohibitive"). The velar nasals (both labialised and not) and the retroflex affricate do not occur word-initially at all.
In terms of clusters that are some interesting restrictions. The set of intervocalic clusters is listed below (in a phonetic transcription):
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ʔ x n p ʔp xp mp t ʔt st nt tʂ ʔtʂ ʂtʂ ɳtʂ c ʔc sʲc ɲc ʔ - xʔ nʔ s ʔs ss ns x ʔx xx - xʷ ʔxʷ xxʷ - m ʔm xm mm n ʔn sn nn ɲ ʔɲ sʲɲ ɲɲ ŋ ʔŋ xŋ ŋŋ ŋʷ ʔŋʷ xŋʷ ŋŋʷ w ʔw - - ɾ ʔɾ xɾ nɾ j ʔj - -
As noted in previous posts, schwa is heavily restricted as a vowel, being somewhat lesser in status relative to the "full vowels" /i ɛ ɑ u/. As noted above it is not found at all before palatal/labialised consonants and clusters including them, and when morphology would produce such an instance the schwa is fronted/rounded to /i/ and /u/ respectively. Furthermore, with a handful of exceptions a root can never contain all schwas: all roots contain at least one full vowel. The exceptions consist of the intensifier particle ‘əŋə, the generic noun tən "thing", and the reflexive pronouns məxən/rəxən, which are formed by adding the 1st and 2nd person prefixes to a base -xən (the singular personal pronouns muwə/ruwə are similarly formed as mə-wə/rə-wə, however the labial glide causes the schwa to round as described above). On the other hand most roots do contain at least one schwa: those that don't commonly are either monosyllabic, such as -un "to be similar to X", or have an environment fitting the conditions for schwa fronting or rounding, e.g. xistyi "leg". The constraint is weak though in bisyllabic roots: it is much more prevalent in trisyllabic roots. However, on the flipside the /ɛ/ is fairly strongly restricted to occurring only once in a root, the only exception being ne‘e‘ "ant".
Obviously without a fully fleshed-out language with a large corpus it's difficult to make any conclusive statements as to frequency, however the following observations can be made. tr is far in a way the most uncommon consonant (and clusters involving it are similarly rare), followed at a distance by xw, ŋw. On the flipside, the most common consonants likely include t, ‘, y, w, however I have much less of a sense of that so I can't be sure just yet. Clusters are even more difficult to guage in this respect. On the other hand when it comes to vowels /ɛ/ is the lest common vowel, which the most common vowels overall are probably /a ə/.