I don't understand has ho been added to the kown family as an adopted brother...? I'm not...

I don’t know what family member ho has been adopted as but I know in countries where gay marriage isn’t legalized yet, it is common for gay people to adopt their partner into their family because that’s the only way they can be considered family without marriage. E.g. when you go to a hospital and they only allow family to visit. Or if they wanted to adopt a child together they could be considered one big family. even if on paper only one of them would be considered the child’s parent, at least they’re family and could make legal decisions for the child. let’s say if the child needed surgery and someone needs to sign off on it, they both could. I’m not too knowledgeable about it but you should definitely research it

it's...complicated. same sex marriage is not legal (yet) in south korea, so haebeom and ho entered into a same sex adult adoption instead. haebeom adopted ho as his son, technically, though for all intents and purposes, they'll treat one another as spouses; the adoption is just a means of legally deeming them family. (it's easier and more practical for haebeom to adopt ho rather than the other way around not only because he's older, but also because ho is an orphan, so he doesn't have to be legally disowned first by his birth parents.) not only does it give them both the right to visit one another in the hospital and make medical decisions on one another's behalf, it also makes them legally one another's heirs (not that they'll have to worry about that for many years, but it'll be important in the long run).

same sex couples in south korea are also not (currently) legally permitted to adopt children together, and since sol's birth father is still alive and obviously very present in her life, it's unlikely that haebeom was able to adopt her as well; though he'll surely act as her second father, my guess is that on paper, she's his granddaughter. she inherited the last name "kwon" from ho, not from haebeom directly.

...all that said, if you were to ask them about it, i'm sure ho and haebeom would not hesitate for a second to call each other husband. (⌒▽⌒)