I just left you a response. I’m pretty sure I found it.
I looked back to see if my message was sending and it turns out it wasn’t there. So here you go. Okay so it took me a minute to find the name. So the name is How To Be A Family (Yaoi).
Here is the link: https://www.mangago.zone/read-manga/how_to_be_a_family/
The Korean name is: 가족이 되는 방법
I was able to find the picture for the second image you were looking for. Here is the link for that episode: https://toonkor465.com/가족이_되는_방법_특별외전_6화.html
It seems that it was the six chapter of the side stories.
Here is the link to the Korean raws: https://toonkor465.com/가족이-되는-방법
When I was doing my research to find the name for this story I found out that it ended last year in July. It seems that the Korean raws go up to chapter 73 with 17 side stories [ so a total of like 90 chapters]. However mangago only goes up to chapter 30.
Also, I’m not sure if my previous message was actually sent, but here you go again.
Could someone help me find the name for this tried to image search but didn't really find anything, not even sure if they're manwhas or only art so if anyone knows anything please let me know ( they're photos on an album on my profile)