
30 days are almost up so about 20 days I think. That's more than enough time to develop feelings for someone, especially when you see them every day and sleep in the same bed too.
He didn't go to his relative's place because they didn't even come for his parent's funeral and he knew he would be unwelcome there so he did have nowhere else to go.

Wanting to live with a stranger is strange I agree but falling for them after more than half a month? Definitely not.
I don't get why you think it isn't natural to be in love with a guy who helped you when you were at your lowest. He can see that Changdeok is grumpy but keeps showing that he actually cares for him through his actions too.
Are you misunderstanding something? He wasn't into Changdeok romantically at the start of the story, his feelings developed gradually.
I would really like to know why he's so in love with him, it can't possibly be just from watching him in the restaurant