Is Eun Byul dead or alive?

My theory if Eun Byul died...

She believed her twin sister should have lived in Seoul instead of her. Her guilt was probably really strong that causes her to hallucinate--> depression--> or even schizophrenic (the washroom episode where she screamed? and the weird paranormal activity around her? and all the hallucination she's been having?). She's cool on the outside but on the inside she's probably really sad/guilty/ depressed even though she has her friends, Yi Ahn, and her mother. THe reason was probably bcuz of Eun Bi. She wanted Eun Bi to live the same life as she is and Eun Byul wanted to escape from her life . She was probably really scared (aka haunting~)and wanted Eun Bi to take her place. 

THere's actually a study of twins that one of the twins have a higher chance of schizophrenia. (studied in psychology)

My Questions: 

1. why didn't they do DNA test right after they found the corpse? 

Why the cremation pot only put the name Lee Eun Bi instead of Go Eun Byul? 

2. OR maybe they believed Eun Bi is dead... but actually she is alive. 

3. Or.. Eun Byul is actually dead in the first place (probably because she was kidnapped/murdered?) and her soul helped Eun Bi out of the water. (wait.. i dun think this makes sense...)

4. Even  if both of them are alive... won't they fight for the same guy?? Yi ahn especially...

In the preview of ep 9, Yi Ahn was looking at the cremation pot of Lee Eun Bi not Eun Byul. Why was he sad when it's not Eun Byul's name on there? I know he is upset believing that Eun Byul is dead. But the hangeul (Korean letter)..is LEE EUN BI not GO EUN BYUL. 

Maybe it was Eun Byul's cremation and they made a mistake with the name? 

My theory if she is alive,

She must be  hiding trying to look for the stalker... she is watching Eun Bi in the shadows. There's too much mysteries around Eun byul. 

She is helping Eun bi by spreading the rumors. We still don't know much abt Eun Byul and Soo In.. but we do know Yi Ahn loved Eun Byul. 

It makes the most sense for Eun Byul is alive!

It doesn't make sense that someone good at swimming will drown, especially after we know that she DID pull out Eun Bi out of the water. Of course the mystery of WHY the police decided that the corpse they found is Eun Bi (there must of found something to think that) is one of the KEYs to solving the mystery.
Another thing we need to find out is WHO is behind this text messages and pranks. As Eun Byul isn't the only one receiving them that means that there was an accident (maybe bullying) that all this people are involved in that led to Soo In to commit suicide. Now someone is taking revenge to the people they think is responsible for Soo In's death - its either her mother or someone she was close to. Soo In's mother clearly knows something as you can see the scary look in her eyes and her sinister smile, she may be well aware that Eun Byul right now is actually Eun Bi.
* This reminds me of 'White Christmas' - where a few students got anonymous notes and they had to solve who was behind it... (I won't give away what happened as its a really good drama to watch, and if you have watched it already you will know what I mean).

Ah, and it doesn't make sense for the SHADOW person (that's how I call the person behind all of this) will actually kidnap or kill Eun Byul - simply because judging from his behaviour he wants her to suffer, and if she dies its over. That means that maybe with the whole accident (Eun Bi trying to kill herself and Eun Byul disappearing) Eun Byul found the perfect option : to exchange with her sister (this giving Eun Bi the chance to live the life that was stolen from her, to
have a mom) and it gives Eun Byul the chance to be in the shadows and try to find out who is behind the messages and pranks.
It is the theory that makes perfect sense, more than the chance of her drowning.

@CindyYan your questions and answers are kind of contradicting:

1. why didn't they do DNA test right after they found the corpse? Why the cremation pot only put the name Lee Eun Bi instead of Go Eun Byul? 
- Well obviously they found something to make them think its Eun Bi, and that's why it her name on the cremation pot.

2. OR maybe they believed Eun Bi is dead... but actually she is alive. 
- Clearly it is....

3. Or.. Eun Byul is actually dead in the first place (probably because she was kidnapped/murdered?) and her soul helped Eun Bi out of the water. (wait.. i dun think this makes sense...)
- It's definitely not Eun Byul's soul/ghost, if you watch closely at the end of the episode (which Eun Bi returned her memories) after the credits there are flash of scenes, in one of them we see Eun Bi on the bridge and Eun Byul is there watching her.

4. Even  if both of them are alive... won't they fight for the same guy?? Yi ahn especially...
- Eun Bi clearly knows that Yi An loves her sister, so I don't think that will happen.

In the preview of ep 9, Yi Ahn was looking at the cremation pot of Lee Eun Bi not Eun Byul. Why was he sad when it's not Eun Byul's name on there? I know he is upset believing that Eun Byul is dead. But the hangeul (Korean letter)..is LEE EUN BI not GO EUN BYUL. 
Maybe it was Eun Byul's cremation and they made a mistake with the name?
- I think you both ask the question, answer it with the next, and then ask the same question.
IF Yi An is looking at the cremation pot that obviously means that Eun Bi told him the truth that she is not Eun Byul and that Eun Byul is dead (that's what they think, they think that the police has identified the body as Eun Bi but since Eun Bi is fine, that means that Eun Byul is dead). SO obviously he will be sad as he believes that its Eun Byul in that cremation pot, no matter whose name is on it. The police has OBVIOUSLY made a mistake identifying the body, we all know that Eun Bi is alive!

I hope that helps. 

After watching the whole drama, did Go Eun Byul died?