
Does anyone know the name in Korean?

yea it’s just 백정, raws go up to ch 15
https://tkor04.com/%EB%B0%B1%EC%A0%95

I just wanna know if they get to see each other again and that she tells him that she is pregnant

This is a 4 years late answer but yes they do get to see each other again. This is also the worst adaptation of this novel that I have seen. The novel is beautiful. If you want a good adaptation that covers all major plot points (though isn't completely faithful to the novel), I would say watch to the drama.
Does anyone know if there will be side stories?????
Since artist directly mentioned alpha trauma after finishing this one. I don't think there will be any side stories ╥﹏╥
Wow just wow. Thank you for telling me that