Let's discuss the plot

I do not think Rang will end up being the big evil but I also think he isn't trying to help his brother. He just wants to mess with him for attention, like you said. 

I'm interested to see why the parents were on the island. I wonder if maybe they did something magical to the baby and that is why DW isn't getting the response he wants from her with the bead thing he is looking for.

I have a feeling her parents got her fortune told and it wasn't good so they went to the island to undo it. That's my first theory anyways. It will probably change.

Episode 3 really made the plot interesting this episode arises several questions ?:

1) Is Ji Ah reincarnation of Ah Eum?

2) If Ji Ah is the reincarnation of Ah Eum why the  fox? bead ? given by Lee Yeon is not there when Lee Yeon tried to search for it inside Ji Ah?

3) Did Ji Ah's parents visited the mysterious island after she was borned ? Is this reason they disappeared?

4)Did Ji Ah's parents knew something related to their daughter like her future . So they sacrificed themselves to save Ji Ah from danger? And do her parents hid the fox bead  ? to save Ji Ah?

5) When Lee Yeon searched for Ah Eum throughout several years ,Did she was born everytime but due to the fox bead ? missing Lee Yeon thought that these women were just dopplanger of Ah Eum?

6)Did Lee Yeon really killed Ah Eum as shown in episode 3 as shown in a glimpse of episode 3 where  Lee Yeon had a sword pointing towards Ah Eum? 

7) Is their a Prophercy related to Ji Ah that forced Ji Ah's parents to hid the fox bead ?? How Ah Eum really died? Was it a conspiracy against Lee Yeon? Who does not want Lee Yeon and his past lover to unite?

8) Who is the baby that Lee Rang gave to an old man in episode 3?

After episode 4  I'm starting to believe Rang doesn't really want to hurt yeon but rather he is doing it because of the debt he has. Also im curious to know why was he finally able to confirm it was her at that moment when before he had tried and it never worked so why now? Also did someone notice that as soon as he confirmed she as his first love the baby or whatever that is opened his eyes.

This is just a theory....but what if ji ah and the "baby" are connected and thats why as soon as the baby was "born" he was finally able to confirm it was her. Im guessing ji ah/ah eum and "he" are connected somehow  

yeah no he isnt acting evil but he is not necessarily evil but rather all the pent up anger he has against his brother abandoning him for a women ect has made him forget his true self, but i do believe deep deep down he is just a little kid who got lost without his brother 

 Aleksandra106:

I agreee that Rang will probably end up helping in the end. He cares for Yeon and he is "the most precious thing in his life" but I believe he will help also because of the "something" he has with Ji Ah.  He said he "likes her from head to toes" when they met and even though he doesn't exactly  care about her I think he is continuously impressed by her, being so smart and brave "for a human girl".  I suspect they may end up as friends. Anyone sees what I see?

yeah i can definitely see Rang growing fond of ji ah but i hope the writers develop it into a strong friendship rather than have him falling for her

I'm only taking a guess based on the minimal almost no research I did. 

First, I think Ji Ah is pretty well rounded, just not in a conventional strong character way people expect from kdramas , and she's fast becoming a memorable lead for me, but that's a whole other post. 

1. I'm assuming going by appearance and outfit alone, that she's the bringer of misfortune in all fairytales.  A universal symbol of sorts: think stepmothers, greedy queens, evil wives. She latches on to the worst memories and plays into them.  I'm also assuming that the snail wife here is not just a reincarnation, but representative of all the classical heroines, the leads.  As for why she went there first, maybe because she hoped to find the Lee brothers and Ji Ah there.  A HUGE HUGE reach, but the absent-minded, slightly pitiful boss of Ji Ah, could be the snail's husband reincarnated.

2. Given that we know her parents are neither living nor dead, that her mum believes/believed in reincarnation, visited the cave where maybe he Imoogi was born perhaps her parents do have ties to the supernatural.  Questions and doubts I have are 

1.  Who actually caused the accident?
2. Who were the foxes imitating her parents before she realizes the truth? So far I'd assumed it was Rang and Yu ri , but I somehow am no longer sure

3. I'm not sure, with the information we have now, it is a reach.  But why would they mention the dead child out of nowhere?  Why would Yeon stress that he's prepared to do anything to save themselves this time around?  But then didn't the granny already say her son committed suicide?

4. I think Yeon is right. When he met ah Eum he maybe spent lesser time with Rang, and with the death of the Imoogi/  Eum, and trying to freeze time, he was damned and probably due a hefty punishment. Which is how I think he winds up working for Granny and the afterlife office. To Rang, this possibly seems like abandoning him.  Even when he hunts him down, and this could be a REACH, but I think he deliberately misses. Only mortally injuring him. At the very start the Granny tells Yeon that he's working a LONG  set of assignments, in return for the life sparred, I'm assuming that life is Rang's.  To 600 odd years younger, half-human abandonment issue filled Rang it probably felt like he was  left alone 

5. The current Imoogi confuses me. In the way that ji ah has a piece of it, does he/it have a part of ji ah's soul now? That would explain saving the sparrow's life,  insisting the rules they play by this time are different 

OK, I think that's about it , this somehow hahaha turned into a mini-essay