1. as far as i know, [ts], [f], [sh], and [k] don’t form or belong to one natural class, although it can be noted that [ts], [f], and [sh] do belong to the [+son] family, whereas [ts], [sh], and [k] are all produced in the alveolar ridge.

2. as for vowel addition to interjections in japanese, i think it’s got something to do with the amount of syllables “permitted” for an interjection or a mimetic expression–especially with mimetic expressions you see words like くんくん where the expression is merely a repetition of one syllable so one would think a single syllable might suffice whgere it doesn’t (or maybe its just a reflection/accurate observation of the actual action itself)

3. what you mentioned as the “vowel” or the “strong consonant” for profanities and what not is actually a part of syllable theory: naturally language prefers sonorous phones over their less sonorous counterparts, and with vowels being the most sonorous of all phones, vowel addition helps stabilize and even amplify the sonority of those less sonorous sounds (i.e. ts, sh) but yeah, your observation is quite accurate in that sense…

by the way another point i might add is that sometimes when you suspect being burned, you say “hot” or “atsui” instead of “shit” or “ow” or “itai”, but often you’ll just say “ow”, “shit” or “itee”; this seems to be true more often in english than in japanese. “ow” and “hot” are both states of pain, yet with the very short, almost reflexive exclamations, we have enough time to make the distinction. oh, and maybe even “tsumetee”, though you seldom see anyone exclaiming “cold!”. heck, cold states might not even be considered pain states in some languages. strange, though i guess this would be more of a philosophical matter than a linguistic one.

also, i wonder if there are phonetic rules to the exclamations? for instance, the onyomi 痛 (tsuu) is suspiciously close to peter griffin’s “tsssssss aughhhhhhhh tssssss aughhhhh”. everything else, atsui, itee, achii, ouch, seems to start with a vowel — even “fuck” or “shit” would usually start with an utterance like “ahh” or “augh”, as in “ah fuck” or “ahh shit”.

then again, i can’t remember the name of the group of phonemes that comprise “ts” “f” “sh” “k” (like the japanese クッ that you see in manga a lot), but they all seem to be attempts to stop a vowel — maybe because letting out a vowel would be loud and potentially panic-inducing to the rest of the people around you, and the buildup of pressure in your mouth is a good way to manifest the pain physically.

the rule (vowel or strong consonant) seems to be true for a lot of profanity too, especially the ones that also double as exclamations of pain — “kuso”, “chikusho”, “fuck”, “shit”, and arguably even “piss”, “ass”, “bob saget” (the “saget” part is probably partly conscious/habitual but the “bob” is probably reflexive), “bitch”, but not “whore”, “idiot”, or — hm, i can’t even think of any.