I think you’re right on maybe he might’ve gotten kicked out because he was gay, the sister didn’t seem to be in love with him or anything and she did ask if he was being inappropriate to him.
As for if they actually slept together or if it was all just in his dreams, I think it might just be that the Brother-in-Law somehow blocks out the fact they’ve been sleeping together? The brother said that the Brother-in-law embraced him every night, so I think the BiL just thinks it’s a dream each time and so he writes it down when in reality they’ve been sleeping together since he arrived.

Bro what's actually happening in chap 4? Is it supposed to be supernatural? Why does it all only feel like a dream?
And I don't really think the brother slept with his half sister he may have said that to spite his in-law my assumption is he got kicked out of his house because he's gay since at one point his sister ask the husband whether her brother did anything disrespectful to him. Then again, I don't really know ( ̄へ ̄)