The whole "they must be brothers because the mum and Bum have the same hair colour" is pretty stupid to say the least. Is the plot not sufficient enough, without adding the tedious incest trope into the mix? Both Sangwoo and Bum have distorted memory when it comes to people and what they looked like, but if he feels that Bum is a replacement for his mother, then yes he would get uneasy when this embodiment of her starts to act sexually aggressive towards him, regardless if he was a victim of sexual abuse from her himself.
No. I don't think they have any relation at all. But that's just my opinion.
The plot regarding the family dynamics of both Sangwoo and Bum is complex/interesting enough without the rather simplistic incest trope being added to tie up all these loose ends. Who knows though what Koogi plans, but it will be a bit of a let down if it ends up they were related. Sangwoo's background of having two abusive parents, one of which he had a codependent relationship which has continued to effect his own mental health is "enough". Ditto with Bum's own background of having to be brought up by his grandparent and uncle who abused him, in light of his own parents deaths.

She looks like bum....bum and sangwoo maybe brothers? I hope not xD