This is something I had not thought of, but it fits into the category (3) to which I had never really payed much attention. My main focus was the ending in -ow.
In your group 1, the English words once had a "g" at the end (or followed by only a single vowel) and lost it, except for "yellow", which is also the only one for which the non-English cognates have something else at the end instead of "g", so it doesn't really belong in the group.
That loss of "g" happened even when the adjacent sound(s) was/were only "a" or "o", so it appears to be a separate rule from the loss(es) of "g" in other places, where it looks dependent on an adjacent front vowel sound. Together, they both seem to be only parts of a complex of Middle English velar-to-non-velar sound shifts:
/ɡ/ ► silent at end in the "-ow" words
/ɣ/ ► /j/ (old sound spelled "g", new sound spelled "y") as already mentioned in this thread
/x/ ► silent after "i" in the "igh" spellings
/x/ ► silent or /f/ after "ou" in the "ough" spellings
/sk/ ► /ʃ/ (as in "shriek/skrik" and "ship/skiff")
/sk/►/ʃ/ is a fun one because I learned to recognize it from Modern English pairs of words in which one was native English with the sound shift and the other was Norse without it, like "shatter/scatter", "shirt/skirt", and even "ship/skiff". A few pairs like that also exist where the import is from French, like "shard/scar". "Skiff" doesn't get much use with most Modern English speakers, but it does among those who are into boating, meaning a smaller class of boats than the big ones we call "ships". Also, a boat's captain can be called its "skipper" in English. All of our modern "sk" words are from Norse or French after their English cognates had become "sh", but the English cognate wasn't always kept, so there's often no such pair anymore (as in "sky", "skull", and "skill").
There was also /k/►/ʧ/ in Old English, as in the pronoun "ic" for "I" already having /ʧ/ in Old English but still /k/ in other Germanic languages. But that was early enough that it would just go silent later on when the other shifts I just listed happened, so it's unlikely to be related to them (unless it was the original trigger which caused the rest as a cascade of side-effects afterward).
Three more develarizations are functionally similar but are French imports, not internal English developments, although the similarities with what happened in English might have made them easier for English to accept without change:
/k/ ► /s/ before front vowels (spelled "c"; later dropping of those front vowels in some French examples led to "ç")
/ɡ/ ► /ʤ/ before front vowels (►/ʒ/ in French)
"ch" spelling ► /ʧ/ (►/ʃ/ in French
What I would like to understand is the phonetic rationale behind the shift (the way Umlaut can be explained by the palatisating/... effect of the ensuing 'j').
I'm not sure what you mean. Palatalization is a change that happened (a shift toward palatal position or under the influence of another sound in or near palatal position), but naming it doesn't tell us why palatalization happened. I don't think sound shifts ever do really have explanations/rationales for why they happened. With the English complex of velar-to-something-else shifts I listed above, we could name the group "develarization", but that would just be another description, not an explanation.
By the way I must admit that I am not that well informed about the historic shifts, except for the First and especially Second Sound Shift.
I don't know what those mean. Are they literal English translations of Dutch phrases? If you mean what English calls the "First Germanic
Sound Shift", it's much more often called Grimm's Law in English, so I infer that the second might mean what we call Verner's Law. (But most sound shifts don't get names like those in any language; there are just too many of them. So they just get descriptions, like "Middle English /u/ diphthongization" for the origin of Modern English's "ou/ow" diphthongs.)
Phonological history of English - Wikipedia
Should you know of a survey of some of the shifts you are referring to, please tell me.
There aren't equivalent Wikipedia articles at the same level of detail about the evolution of other modern languages, at least not in English, but maybe there are in their own languages. Below is one for Proto-Germanic which is also more detailed than what most other past languages get in English, again presumably because English is Germanic; maybe similar articles on other past languages exist in their own nearest modern relatives...
Proto-Germanic language - Wikipedia