Katty brings up a good point... Perhaps in his younger years he was an outcast, but as he became famous everyone began fawning over him. This would certainly be enough to make Krum even surlier and more withdrawn; after all, I'm sure it can't be pleasant knowing that people only like you because you're good at Quidditch.
I like the idea of the Muggle mother, actually; I don't think that would be at all difficult to believe, and like SiriuslyMental (sorry, I don't know your name ) said, there wouldn't be enough Purebloods to populate the school. In fact, I'm sure that Purebloods would be a minority; I don't think he would be overly discriminated for being a Half-Blood (at Hogwarts, it's only Muggle-borns who are picked on--not Half-Bloods).
The story mostly is before he earns his Quidditch fame. For a long time he is an outcast, very studious. I'm going by the book description here in saying that he's no Louis Prades when it comes to appearance, so he's probaboy not noticed by too many girls. And then he skyrockets to fame when the Quidditch thing sets in, and it's a major thing for him to suddenly find all of these people scrambling to be his best friend, but he doesn't want that. He pulls away from it.
I see him as being humbly brought up - communal housing type thing, long queues for food, youth clubs that he hated, maybe a Muggle sport like boxing, which one of his family may have pushed on him, very observative and clever, but few friends. And then he starts making money and gaining in fame. Suddenly there are fan clubs springing up in England, and commercial business brings some cash flow to his family, now liberated from the communist government and welcome to the income. I see his parents embracing the idea of fame and fortune more than Viktor, who seems shy and not very articulate.
The fact that Durmstrang's very far north means it's not in Bulgaria...but it draws students from Bulgaria, which could support the argument that it ONLY accepts purebloods. If it draws from all over Eastern Europe (and maybe even the West--Draco almost went there, remember), it has a larger pool than say, Hogwarts, which would allow it to be more selective. I would call it a stretch to say Krum had anything less than half blood parents.
As for the being an outcast, maybe Quidditch is his passion and he shuts out everything else? Personally, all the prodigies I know are outcasts anyways. They're a little bit stuck up just because they're really good at one thing, which sometimes causes them to be rejected. Maybe you could have Viktor's peers reject him sort if in anticipation to this stuck-up...ness. Maybe they figure he'll be a jerk since he's so good at Quidditch and they think he probably thinks the world of himself. However, I agree that Krum probably wouldn't be an outcast. He seemed popular enough during his brief cameo in GoF. Perhaps, for your purposes, he could "feel" like an outcast. Maybe (agreeing with what Fenn said) the relationships he has with his friends are somewhat shallow, aka they only like him cause he's good at Quidditch.
As for your desire to set this in Russia, you might just have to take up a research project on Bulgaria. It'll probably be very fascinating.
I love Krum. He's a character I've been meaning to write about for quite some time now, so I just had to say something in his thread, despite the fact that it looks like it's been 'sleeping.'
Haha, thanks. Yes I've been researching, and I'm in love with Eastern Europe now. Lol.
But for Krum being an outcast, in my fic he really wasn't well known until he was 15/16. So, before that he sort of kept his flying to himself. He knew that he was better than anyone on the team, so he was somewhat cocky about it, but he was also very quiet. He would watch school matches and it made him want to keep his own talent a secret even more, because he didn't want to have to play in a school match. He knows that he is professional level and wants to play on that and that alone, so the school mostly sees him as very quiet, somewhat stuck on himself, but also intelligent. He wans't uncool or made fun of for being "outside the fire" so to speak, but he just didn't talk to people much. So, in that sense he was an outcast. It's like, the students finally got tired of trying to talk to someone who didn't talk back and just gave up, but they don't make fun of him or anything.