Was it revealed in the novel that the baby was Ido's? Will they also have children in this life?
They will talk about it in the current timeline. Ido will confirm that Sejin's child was his. I'm not sure if they will have children. There's nothing in the side stories.
Was it confirmed in the first life after Sejin's body was examined?
They didn't elaborate on how Ido knew it was his but that's probably the case. Like post mortem examination.
Even the past was a series of misunderstandings. Ido wasn't planning on having his brother find Sejin do all that but it was misconstrued by his brother when he found Sejin there and by Sejin as well because of what the brother said.
Honestly, this was such a well-written novel. The author redeemed Ido before unveiling their messy past that's why the angst hit harder. This is Cozy Obsession if the ML was sane enough to reflect and let go.
What I like about Ido is his development. He gave everything that Sejin need to escape him and his previous life so that Sejin wouldn't leave in misery. What I love about Sejin on the other hand is his capacity to choose himself with grace instead of falling back into Ido's arms without processing the memories he retrieved.
Btw, their child in their previous life was Ido's. Not his brother's.