If just the drama, then possible she wants the returnee student's help in solving her case.
However, since this is a story set in a Shared Universe, she's probably a character from another work. I've read others mention she could be a character from Timing.
Here are Kang's Super Universe (supernatural/superhero) works:
He didn't remember her in the afterlife world, she told him their story then sent him to find his light, he went…
She didn't. For the couple, she's the only one who can remember, while the guy has completely forgotten her. It's the "punishment" for the girl's suicide.
In addition to that, when she stitched him, she went to places which were significant to them, but never returned to the same place. She even said she's running out of places to stitch him.
This hints that her stitching him is absorbing the positive energy and memories they built together. It can be the very reason why when the guy returned to life, he failed to remember her still even though the evidence is right in front of him (the phone). Their memories were used for stitching him.
If Hyun Min remembered his girlfriend (the moment before he grabbed the light bulb) why did he decide to leave?And…
He did not exactly remember. It is common in real life that when someone is told that they've been in an accident and they've forgotten things, like their spouse, they become very hurt, and sometimes blame themselves. They feel very guilty because they can't remember the person in front of them who loves them. Some will do everything loke pretend, or get to know them again in the dopes that they'll eventually remember or fall in love again.
In this show, they guy tried that. He believes her story. He felt guilty he can't remember the lovely person in front of him. The love of his life. Who weet to so much trouble to stitch him so he can live.
Eventually, when he returned to life, he even saw proof of her story. But, like anyone who experienced amnesia, he can't remember and thus he continually felt guilty about it. He believes her.
That's all there is to it. They simply added a superstition and fictional trope to it in the form of "suicide", which in many cultures is, wellโฆ you know.
He's not suffering from delirium, he took the position of the person in the restaurant. The person in the restaurant's…
The lady growing tall was not irrelevant. She's dead, she's lost. She's angry. When she grew tall and scary, it was her "revengeful" side trying to unleash itself.
However, when her girlfriend arrived at the house she's hiding, that's when things changed for her. She started to remember. She started to gain control. And when her girlfriend remembered her, she stopped being a revengeful shadow and regained her human-like appearance and personality.
Then the bus driver apologised and she accepted it.
Finally, her girlfriend returned and chose her, which finally sealed away her revengeful spirit.
Everything is important and has meaning. The writer is an experienced writer. He was also the one who created the webtoon the series was based from. He is considered as one of the pioneers in the webtoon industry.
These are all his works set in the Super Universe (supernatural/superhero).
He's not suffering from delirium, he took the position of the person in the restaurant. The person in the restaurant's…
"Weird things are happening to his eyes". That's a natural effect for being hit in the head. Yes, it is real. There are certain instances wherein if you got hot in the head, it can damage your control over your eyes, and occasionally does that. It's rare, usually a person just die with such a head blunt.
That movement of his eyes is not supernatural. It has nothing to do with his serpent eyes in E08.
This show is a mess and it's totally unhinged. So is the police detective also suffering from delirium since only…
"Delirium" is the official terminology by doctors to anyone thinking they were in another world. It's an "excuse" to explain the unexplainable.
It doesn't mean that they were actually delirious. As we all know, all of them literally came from the Afterlife/Limbo world, where the border between life and death is.
None of them were delirious. They were just treated for delirium because the scientific community doesn't deal with the supernatural and make excuses about it like delirium.
As for your second question, the Detective took on a special job, to hunt ghosts crossing over with revenge intentions, like that truck driver miss Nurse told to wait.
The nurse and the student/daughter did not receive that task, so their eyes are normal. They can see ghosts because they've seen death or were close to it. (It is a common tropi in fiction, which came from superstitions and fringe science.)
1 
If just the drama, then possible she wants the returnee student's help in solving her case.
However, since this is a story set in a Shared Universe, she's probably a character from another work. I've read others mention she could be a character from Timing.
Here are Kang's Super Universe (supernatural/superhero) works:
์ํํธ (2004) Apartment
ํ์ด๋ฐ (2005) Timing
์ด์์ฌ๋ (2008) Neighbor
์ด๊ฒ์ธ (2009) Again
์กฐ๋ช ๊ฐ๊ฒ (2011) Light Shop
๋ฌด๋น (2015) Moving
๋ธ๋ฆฟ์ง (2017) Bridge
ํ๋ (TBA) Hidden
This is Kang's Super Universe (supernatural/superhero).
์ํํธ (2004) Apartment
ํ์ด๋ฐ (2005) Timing
์ด์์ฌ๋ (2008) Neighbor
์ด๊ฒ์ธ (2009) Again
์กฐ๋ช ๊ฐ๊ฒ (2011) Light Shop
๋ฌด๋น (2015) Moving
๋ธ๋ฆฟ์ง (2017) Bridge
ํ๋ (TBA) Hidden
In addition to that, when she stitched him, she went to places which were significant to them, but never returned to the same place. She even said she's running out of places to stitch him.
This hints that her stitching him is absorbing the positive energy and memories they built together. It can be the very reason why when the guy returned to life, he failed to remember her still even though the evidence is right in front of him (the phone). Their memories were used for stitching him.
I've read that the detective as well.
The ghost student is supposed to be the one from Kang's ยซTimingยป.
In this show, they guy tried that. He believes her story. He felt guilty he can't remember the lovely person in front of him. The love of his life. Who weet to so much trouble to stitch him so he can live.
Eventually, when he returned to life, he even saw proof of her story. But, like anyone who experienced amnesia, he can't remember and thus he continually felt guilty about it. He believes her.
That's all there is to it. They simply added a superstition and fictional trope to it in the form of "suicide", which in many cultures is, wellโฆ you know.
However, when her girlfriend arrived at the house she's hiding, that's when things changed for her. She started to remember. She started to gain control. And when her girlfriend remembered her, she stopped being a revengeful shadow and regained her human-like appearance and personality.
Then the bus driver apologised and she accepted it.
Finally, her girlfriend returned and chose her, which finally sealed away her revengeful spirit.
Everything is important and has meaning. The writer is an experienced writer. He was also the one who created the webtoon the series was based from. He is considered as one of the pioneers in the webtoon industry.
These are all his works set in the Super Universe (supernatural/superhero).
์ํํธ (2004) Apartment
ํ์ด๋ฐ (2005) Timing
์ด์์ฌ๋ (2008) Neighbor
์ด๊ฒ์ธ (2009) Again
์กฐ๋ช ๊ฐ๊ฒ (2011) Light Shop
๋ฌด๋น (2015) Moving
๋ธ๋ฆฟ์ง (2017) Bridge
ํ๋ (TBA) Hidden
They're all interconnected.
That movement of his eyes is not supernatural. It has nothing to do with his serpent eyes in E08.
It doesn't mean that they were actually delirious. As we all know, all of them literally came from the Afterlife/Limbo world, where the border between life and death is.
None of them were delirious. They were just treated for delirium because the scientific community doesn't deal with the supernatural and make excuses about it like delirium.
As for your second question, the Detective took on a special job, to hunt ghosts crossing over with revenge intentions, like that truck driver miss Nurse told to wait.
The nurse and the student/daughter did not receive that task, so their eyes are normal. They can see ghosts because they've seen death or were close to it. (It is a common tropi in fiction, which came from superstitions and fringe science.)
์ํํธ (2004) Apartment
ํ์ด๋ฐ (2005) Timing
์ด์์ฌ๋ (2008) Neighbor
์ด๊ฒ์ธ (2009) Again
์กฐ๋ช ๊ฐ๊ฒ (2011) Light Shop
๋ฌด๋น (2015) Moving
๋ธ๋ฆฟ์ง (2017) Bridge
ํ๋ (TBA) Hidden
Shared universes are not new, the MCU thing was not the first. ๐
์ํํธ (2004) Apartment
ํ์ด๋ฐ (2005) Timing
์ด์์ฌ๋ (2008) Neighbor
์ด๊ฒ์ธ (2009) Again
์กฐ๋ช ๊ฐ๊ฒ (2011) Light Shop
๋ฌด๋น (2015) Moving
๋ธ๋ฆฟ์ง (2017) Bridge
ํ๋ (TBA) Hidden
์ํํธ (2004) Apartment
ํ์ด๋ฐ (2005) Timing
์ด์์ฌ๋ (2008) Neighbor
์ด๊ฒ์ธ (2009) Again
์กฐ๋ช ๊ฐ๊ฒ (2011) Light Shop
๋ฌด๋น (2015) Moving
๋ธ๋ฆฟ์ง (2017) Bridge
ํ๋ (TBA) Hidden