In compiling the description of a language, a grammarian can choose to omit irregular variants (contracted forms, etc.), making the grammar of that language seem more regular, or he can choose to include them, making it seem more irregular.
He can also choose to designate certain word variations as "derivational", and others as "inflectional". The latter choice can potentially make a language seem more irregular than it otherwise would: for example, if the imperfective/perfective alternation in Slavic is considered inflectional rather than derivational or lexical, it hugely increases the perceived irregularity of the Slavic languages.
So, I don't necessarily agree that "irregularity is irregularity": the regularity and irregularity seen in inflectional tables can reflect the biases of the grammarian(s) who first compiled them.
"are definitely conjugated/declined forms"? I don't share your certainty here: inflectional tables are products of grammarians' methodologies, not obvious and transparent reflections of reality.
(I am not saying that inflectional tables don't reflect reality at all, but I think that their accuracy should be gauged in terms of whether they can help you read, understand and/or communicate in a given language.)
It's at least part of the issue. Agglutinativity is a straightforward ("1-to-1") correspondence between meaning and morpheme; fusionality makes this correspondence less straightforward (though it is not the only way of doing so).
You mentioned that Georgian is agglutinative despite its verbal irregularities: if these irregular processes disrupt the 1-to-1 correspondence between morphemes and meanings, then maybe it is more accurate to call these processes fusional. A language can be fusional in some areas and agglutinative in others.
Can you elaborate on "controlled classes if irregular in a way"? Some specific examples would be helpful.
I have explained it before, sound change is only a fraction of why IE languages are exceptionally irregular. If there are multiple unpredictable ways to form a different case or tenses, not one way to form a tense that gets obscured by sound change, they were all separate formations.
Georgian has some fused forms but most of its irregularity manifests in unpredictable thematic suffix extensions in some verb forms where the extension can be one of several separate ones, the fact the future is formed with a prefix that must be learned by heart, and by changes in transitivity classes in some verb forms etc.
Controlled classes refers to the fact languages in the rest of the world may have an irregular or complicated area but said area is made of only a limited amount of stems such as navajo with only 550 underived verb/adjectives. Even if the verb system is not closed, languages outside of Europe or not influenced by IE tend to have their less morphologically elaborated sides such as Georgian being genderless and with only 1 declension or Navajo having nominals even simpler than English and no separate adjectives.
Learning Arabic, Korean, Georgian, or Navajo involves learning complicated systems and applying them with easier sides of the languages, like climbing a hill to reach the summit. Learning Russian or Ancient Greek can be liked to climbing a hill only to find there is another hill one after the other with further walls of stone along the ways followed by another hill.
1. Whether a Latin 3rd-declension adjective takes -er, -is, -e or -is, -is, -e is generally quite apparent. You can tell upon seeing the adjective for the first time. I don't know what you're talking about with irregular ablative forms, but the ending is -i (singular) for every single third declension adjective except vetus, veteris, which acts like a noun and takes -e
2. Not sure what "loan any flexibility" is supposed to mean... the masculine, feminine, and neuter cases only differ in nominative and sometimes accusative, and they do it in a predictable fashion.
3. Comparatives are formed by dropping the ending and adding -ior for m/f and -ius for neuter. The only irregularities are with a few adjectives that are irregular in English, too.
4. Again, comparatives are regular.
5. Perfect stems are unpredictable in every conjugation except the first, yes. However, they do form in regular and semi-predictable patterns. Someone familiar with the language can often correctly guess the perfect stem of a new verb if given the present.
6. -io verbs aren't irregular, just another part of morphology (which you said doesn't count as irregularity), only perfect passive participles are irregular (but like the perfect stem, semi-predictably so), missing forms only apply to fewer than 10 verbs, deponent verbs actual express a voice other than active and passive which has since disappeared (so they're not irregular, just a part of morphology), and we're not talking about Russian.
7. Nouns are almost entirely regular as long as you know the declensions (again, that's just morphology). There are only a handful of irregular ones.
8. Not sure how this is relevant. There's no issue with what you're describing in Latin.
9. There are not "page upon page" of irregularities. I could fit them all on one page
10. Only two cases govern prepositions, so naturally prepositions are needed. There are far more prepositional concepts than cases, so it makes sense to have two general cases that give the sense of how each preposition functions.
11. English prepositions are used very irregularly. Latin has extremely regular prepositional use. especially compared to German and English.
I should also like to point out that instead of comparing one IE and one non-IE language, you are picking one IE language and then several non-IE languages, choosing languages that are non-irregular in the grammatical/morphological realm being discussed. For instance, if you want to compare Arabic and Latin, you need to point out that Arabic plurals are far more pervasively irregular than the Latin case system.
-An adjective ending in -er could be 1st or 3rd, but even if its all predictable, no other language has adjective suffixes are exception filled and irregular as Latin. Arabic has its broken plurals but the other parts of its morphology are not as complex.
-Comparative irregularities are more than that of English, and comparative irregularities are absent completely in most other language families, its not universal.
-Even if there are rules for latin adjectives, these complexities simply don't exist elsewhere, IE adjectives were modified by derivation and continue to systemize to this day.
-Perfect stems are unpredictable, there are tendencies, but the perfect stem is formed multiple ways, it originated as a separate lexical word and so did the non-finite forms, that's why many Slavic presents are not predictable from their infinitives. Like I have said before, it is not sound change here, and Indo European verbs were not a closed controlled systemized class like Navajo.
-This also explains why the future was formed differently in conjugation 1 and 2 and another way in 3 and 4, the future originated also as a lexical word.
-Fair enough about the cases, the stems are not what I was referring to but the different amounts of suffixes. Its not that corpus-corporis, but portui but cornu, portibus but artubus, ae/i/u/s/ all being different suffixes for one case. Arabic/Sanskrit/Korean case suffixes tend to remain constant except for some sound changes here and there and Arabic has broken plurals (but plenty of other areas in its grammar that make it very regular compared to Russian/Ancient Greek types).
I also mentioned Chechen, where extentions are added randomly in nouns such as "biesh-bieshuo-biesham
azh" while "kuotam-kuotamuo-kuotamazh" reconstructions show the suffixes are not fused forms but separate morphemes, they originated as derivational suffixes for nouns the way we prefix verbs but when cases and plurals were created they used them to create the new forms, its not sound change here.