This is to clarify some issues present within both series, and to remind new readers and editors going in about some things. Not as any attack, but to help to explain edits I make and to anyone unfamiliar with either series.
1. "Osomatsu-san" is not meant as a direct sequel to -kun. It’s more of a re-imagining. Knowing -kun is a bonus, especially for certain characters. But you don't have to absolutely know it either. If you feel inspired to watch or read it thanks to -san, you should give it a try.
In general, it's like -kun might as well not matter to -san, despite the few bone-throws to it in season 2. The series composition writer was hired without having read -kun, and the director saw this as a must for the series to appeal to the mainstream crowd and new viewers, and not any people nostalgic for the series. This is why Iyami and Chibita were also pushed back, since it was thought they could no longer be interesting if the Matsunos now had personalities. There are pros and cons to that whole idea, as you can imagine.
The staff seemed to deliberately go out of their way to avoid ever referencing "the past" beyond some gags, and the boys' childhood photo album being "Sealed" (banned) was indication they weren't ever going to tell viewers how exactly they got from their 10-year old selves to NEETs or what their junior high and senior high years were ever like. To the staff, -kun's past is not the important factor, the characters you see in "-san" are what matter and how they are. This is why -kun skits are remade as -san, why characters like Kinko are recreated as entirely new people.
If it were a full-on sequel, it probably would be treated a little differently even if some things would have to remain the same, like the general lack of continuity between skits, a certain status quo, etc.
2. The order of the sextuplets was actually never settled or consistent in the manga. It's confusing but true.
Oso-Kara-Choro-Ichi-Jyushi-Todo is what Fujio Pro has gone with since 2008 based off the 1988 ending (aside from Jyushi and Todo’s placements), but it doesn’t necessarily mean that’s what Akatsuka had in mind. At this point, that doesn’t matter but it’s still important to clarify that.
If you wonder why the order’s different in some early manga role-calls, or who’s oldest or youngest, there is no clear answer. But trying to retrofit Karamatsu to be “Second-oldest” in all references about him is just going to get people confused, especially when there’s no birth order hierarchy in the older stuff.
The 1988 show might have even had a specific order in its ending sequence, but it never used that itself in the episodes. It’s more common for you to see the boys grouped off by their combis, or by certain trios, than it is to get them lined up Oso-Kara-Choro-etc. or even Oso-Ichi-Kara-etc. (which Matsuyo still yells at times).
3. Characters’ alignments and some details can and will change depending on the story. Families can change. Ages can even change if the story so demands it. There is no one “canon” or a solid continuity beyond some things that are a usual status quo for stories (eg: sextuplets must be grade-school kids/NEETs, they like Totoko, etc.). That goes for both -kun and -san, all versions really.
I understand some would love a solid continuity, and I’m not trying to knock that or anyone against certain stories/episodes where things could have been written better. But sometimes it's not as always simple as an objective “canon fail”.
In many fandoms, there already can be overuse and misuse of the concept of "retcon", and some simple things treated as serious business where you wouldn’t see this kind of attitude if the characters didn’t look as humanoid. Well, you probably would in some Disney circles, but others have rolled with the expectations that characters aren’t to be held to one role or type of story and that you should expect both deliberate changes in settings and some oddball cases of early inconsistency.
For instance, Aida and Sacchi's relationship in regards to Todomatsu is subject to Matsubara's whim for a skit as some other things would be, so to wonder how they could even want to be seen with him again...well, aside from some nods to season 1, season 2 was indeed kind of a "slate wipe". Some things are very different than how Fujita and Matsubara would have done them in season 1. It's said that any leftover ideas from season 1 were even thrown out, for this to be all-new. I guess that's why the "Carefree Feeling" drama CDs happened.
I figure things like them not answering him on LINE or ESP Kitty's medicine wearing off were some nods of "continuity" but also quick explanations to throw back to those skits and explain why certain things wouldn't be utilized again. But there was no need for that after a while. You just figure it's whatever is necessary for the skit, unless you can come up with your own ideas.
As far as things like "timelines" go and writing about them, it's best to not take s2e1 too seriously. Like the first episode of season 1, they did what they did all what they did to set things up as wildly as possible. They just don't throw you right in with a low-key episode. As the show's all just skits itself (besides whatever things they'll bring up as nods), the sextuplets you see in that episode are all pretty much the same people. The staff wouldn't have thought so far as to consider things as "Timeline A" "Timeline B" etc. It's just wiped clean, as Akatsuka would each time in his manga. But for fanworks, yes, that's a good concept to consider if you wished to delve deep.
If there are any other issues to clarify, please let me know! They can also be asked in "Questions and Answers" forum.