@Amaya19 It takes a bit of time to understand the premises of the story.
Basically, the 1st Couple and the 3rd Couple aren't connected, at all, they pretty much have never met based on what the manga shows, the Radio Host, the Cafe Worker, the Tatto Guy and the Cat Salary Man just never met, their only connection is that the 4 of them are acquainted whit the 4th couple and kinda the 3rd couple (Boss and Yakuza Son).
How ? Simple.
The Tatto Guy was connected whit the Yakuza family in the story somehow since a young age, and was "friends" whit the Yakuza Son, Boss and his Brother (so the Pianist/Cafe Owner by do process) in Highschool, eventually becoming their Neighbor as a "bodyguard" for the Yakuza Son since the 4th couple has a strange arrangement of living together and has a not so healthy relationship, hence why he asks them to take care of the Cat, as they are acquittances and trust each other, later having the Yakuza Son sulking at the Tatto guy house and doing the kissing him thing because of the whole drama.
The Radio Host and the Cafe Worker (Not owner, sorry) simply knows the 4th couple since they frequent the Cafe because it is owned by the Pianist/Cafe Owner who dated Bosses brother (the one who died) and eventually became acquainted whit the Yakuza Subordinate who works under Boss and began a sex-friends relationship whit him, also making the 2 of them acquainted whit the 2nd couple since the guy kinda works for him and the Yakuza Subordinate visits the Cafe to see the Pianist/Cafe Owner.
So, if we go by a simple overview:
1st Couple Knows: 2nd Couple and 4th Couple.
2nd Couple Knows: 1st Couple and 4nd Couple.
3rd Couple Knows: 4th Couple.
4th Couple Knows: Everyone.
So, as you can see, the 3rd Couple is the most disconnected from the group, whit the 1st couple knowing 2 of the couples because they became acquainted whit them because of the Cafe.
Overall, the 3rd Couple is a Plot Device, the 4th couple needed someone who wasn't in a relationship to fit into the drama of the 4th couple, so the 3rd couple was that, a highschool friend/neighbor of Boss and Yakuza Son that wasn't dating anyone BUT that was already in love whit someone (The Cat Salaryman), making it possible for the kiss drama to happen whiteout either of the couples breaking off and also showing us that the Tatto guy is pretty serious about the Cat Salaryman, to the point of actually feeling extremely guilty despite the kiss not being his fault (Tatto guy is a 10/10 men).
So yea, hope that answers your questions, the whole Cat thing had a meaning, it was to establish that the Tatto Guy was not only the Neighbor but someone who knew the 4th couple enough to entrust them whit helping him take care of a cat wen he is not around.
And no, the Radio Host was not acquainted whit the dead guy, at all, only people acquainted whit the dead brother are: Boss (brother), Pianist/Cafe Owner (ex-lover-ish), Tatto Guy (friend), whit the Yakuza Son being the one who was in the accident where he died.
If you still have questions, I can try to explain how the couples became a thing if you also didnt really get that.