Warning: My whole post is spoiler-ific.
1. Karin is Yuri's mother. at one point Anastasia applied for Karin to have goodwill papers from Russia under the name "Anne". You can see this in a cutscene when they left the Battleship Mikasa, after the old man Kawashima pulled some strings to free them. The theory among many people who complete SH:C is that she still had those papers and decided to live as Anne when she travelled back in time.
2. What you got was the good ending, Yuri dies with his memories intact. In the bad ending, he decides to live by sacrificing his memories. He returns to wales an empty shell of a man, who doesn't even remember his own name.
Here's the meaning of the three endings, from Matsuzo Machida, head of development in Nautilus. It was included in the Japanese guide and was translated to English by some guy at gamefaqs. I took this from there, so credit goes to the guy who wrote the FAQ, Sicondera.
.:YURI'S "GOOD" ENDING:.
In the "Good Ending", Yuri watches his friends disappear one by one, each going
to the place they most wanted to be. He never lets on about his own decision,
to bring his life to a close there on the Plains.
He was running. He was desperately trying to escape the terrifying turn his
life had taken. He was *way* out of character... or so say the many letters
we have received on the matter. That certainly seems the case, if you think
Yuri was just giving up so he could get off easy.
But Yuri did *not* give up his fight. The curse of the Holy Mistletoe is
absolute. Yuri would, no matter what, lose all of his memories just a few
moments later. Every single last fragment of the life he'd lived would be
eaten away by the curse. All the days he spent with his friends and the fights
he fought at their side-- gone. Alice, and his bottomless love for her--
erased. Everything, reset as if it had never been.
That's the situation Yuri was facing. Drain from a person his memories and
beliefs. What does that leave? Think about it for a second. Scary, isn't it.
Take memory, belief and thought, ball them up and tie them together with the
desire to live life to it's fullest and you get something which has, to my
mind, value at least equal to that of life itself. Flip that around, and you
have the idea that, being alive, you have the obligation to think for yourself
and live a life you won't regret.
Yuri made the decision to die after he talked with Alice in the train. He
chose to protect the life she'd given him through death. It's a difficult
concept to grasp. I'm sure Yuri had worries over whether or not he'd be
understood.
.:YURI'S "BAD" ENDING:.
On the other hand, "Bad" Ending Yuri chooses to preserve his existance at the
cost of his memories. They buy him a small glimmer of hope-- that maybe,
someday, he'll be able to recover them. Or so it's implied. But I just want
to make one thing clear for you. Yuri will *NEVER* be the same again!
If, in the future, someone else decides to continue this story, they might try
that idea, but in my mind Yuri can never recover completely. If he could, that
would horribly cheapen Yuri's suffering, the terror of the curse, Alice's
death and Karin's love.
Still, there is something to be said for a quiet, peaceful life. Perhaps Yuri
will eventually have some new adventures with Roger Bacon.
.:KARIN'S ENDING:.
No matter how much she loved him, Karin knew she could never replace Alice in
Yuri's heart, and that caused her no small amount of pain. Ironically, that
single-minded devotion to a woman was part of what charmed her about him. I
think she, too, wanted to know what it was like to be loved like that.
In her Ending, Karin had just finished internalizing all the pain and heart-
ache she felt over Yuri when she met his father, Ben Hyuga. It's not portrayed
in the game, but as she spends time with Ben, she puts all of what is
technically her future (the events of 1915), into her past. To get on with
her life and discover her happiness, she chooses to live life as "Anne".
I don't think Karin's the type of person to fret much over why she was sent to
the past, nor talk much on who she was. She'd probably stay silent on the
whole affair. I don't think Ben would press her for answers she wouldn't
willingly give, either. I mean, he *is* Yuri's father. He'd be cool like
that.
However, I do want to clear one thing up. Karin was in no way "compromising"
with Ben. She didn't decide to stay with him only so she could see Yuri. She
honestly and truly fell in love with Ben, and as a result, Yuri was born. You
may have noticed it during Yuri's conversations with his dad, but Ben and Karin
were head over heels in love with each other.
In the end, I think Karin found her ultimate happiness.
Alice did understand him, though. She had from the beginning. She did once
say "Don't worry. I don't mind, no matter what the curse." Even if you forget
who you are, my love for you will still exist. No one can take that from me.
So I don't mind. Even if you choose death, it is the path you have chosen, and
I will abide by it. Besides, didn't I once choose death to protect the soul
which is you? ...that's what Alice was talking about.
To Yuri, his most precious things are the soul that Alice loved, and the heart
that loved her. Nothing else mattered. Protecting those things was everything
to him. It was his "happiness". If he were so weak-willed as to let some
weed's curse steal that away, he would have fallen for Karin's selfless
devotion and forgotten all about Alice long ago.
The time is 1913. Again. Perhaps for the third time? Or maybe the fourth.
Yuri is in China, waiting for That Train. It's the one place his subconscious
truly wished to be. This time around, maybe he really would create a future
he could share, living, with his beloved.