Do I continue reading it or not?

I haven't read this yet so idk the context but illegitimate lineage just means a noble banging a person of non-nobility to create a child.

That child would then be called an illegitimate child

This story is actually very, very slow. But it is quite a good read (if you got nothing else more pressing to read at the moment). But yea, since it progressed so slow, it can be boring too.

"Also I didn’t like how she forgives her father easily like what? He literally said you changed that’s why he asked about her opinion!! Wtf." -- That scene will be further explained through some back story in the Duke's POV in Chapter 102 - 103 (which is S2 finale).

"I’m confused she said she’s illegitimate child and before said her biological father is in coma? How is that!!!" -- Her soul was brought from modern days South Korea to enter a 'novel' she supposedly read, where she became Elodie Perdia, a villain in the novel. Elodie was taken in as 'illegitimate' daughter of the Duke, while later on in the novel, it would be explained that Elodie was actually not the Duke's biological daughter, but another Duke's biological daughter, i.e. Duke Severes, who was in a coma. No, they did not explain yet WHY he was in that coma or HOW to wake him up (yea, like I said the story is slow, convoluted, too much plot, and Duke Severes coma had not yet been given the back story by the time we reach chapter 103).