You sound like you're in the same position as I am, minus the school since I no longer go to one. My work is pretty mundane. I don't get along with people at work much since they are older and my interest are not similar to them. The only time I get to make friends outside work is when I go to gym. But it's hard to establish friendship in a non-permanent setting like that. You have to really make a conscious effort at it. I wish I had made more of an effort during HS/college at making friends.
So I wouldn't completely discount school friends if I were you. Well, it kind of sucks for you now from the sound of it since you don't have similarities to many people. But I'd recommend to try again once you go into college (the best time to make friends - I can't believe I squandered that too). I am jealous when I see people making friends in college now. As for the other stuff, that's why I don't think it'd hurt you to play online games once in a while. Maybe by doing that you can find similar-minded people? Once you get to college, there's usually an anime/manga club so maybe try to join that.
That feeling of loneliness and disconnect you feel now will intensify once you hit mid 30s like I do. Only now I don't have the means/resources/avenue to fix the path already laid out in front of me. I can go and join short courses (ie. taking Japanese class) but that requires money, which I don't have much atm. But you still have more chances/avenues to find friends so don't pass it up no matter how hard it seems to connect with people. Try and try again even if you fail. And if you can, maybe get out of that area you're living now. That's all that I can say in this matter.
That's definitely one difference. I usually get along with everyone, regardless of their age. Most of the time, older people(40+) are better because younger ones tend to only care about their smartphone/facebooks and such.
"But it's hard to establish friendship in a non-permanent setting like that." <---definitely agree with that statement
As I said, I'm already at that "after school" point of life. Been 13 years in school, that should be enough. After that, you either go into training(school+work, what I'm doing now), or you go to a university(can still go there after finishing the training but wouldn't really know what subjects to pick) and study some more, if you are qualified for that. And as for my current school, it's really far away, takes me several hours to get there by train. Work isn't really close by either...not that I want to spend time with them outside of work anyway. In that regard, things won't change for another year until I finish my training. Then I will also probably move to a proper city(we have around 600 people living in this village). I do play online-games, as mentioned. My time with MMOGs may be over(played a lot of them but only ever 1 or 2 months before I grew tired) but I still played World of Tanks from time to time. And while I'm a rather good play(in general), I never bothered with a clan or platoon play. Anyway, the company fucked up around 2 months ago and now I can't play anymore without getting huge lags. So that was that then. I wouldn't mind playing an MMOG again if it's interesting, but I would only consider p2p games, without any micro-transactions. The problem is that my time isn't really there anymore. Work + time to get there and back + buying food and stuff + keeping the house decently(I live alone) doesn't allow for much. So during the week, I'm usually tired and just listen to some rollplaying-videos.
I actually don't have a feeling of disconnect and loneliness. That maybe was the case during the time between school and training but it just went away. Moving away is definitely a requirement but I doubt it's gonna change much since all I will do in a city is go to work and buy things at the supermarket. Best chance for me to get to know people around me is randomly in some national forum but so far, I'm fine with that. I need to eventually take Japanese classes as well but, like you, I need money and also move to a proper place first. All those Japanese games left unplayed, all those good Manga that never get translated. And then this nice chunk of the internet that will be open to exploring. Further, let's not forget the need to visit Japan before their culture deteriorates even further.
Apart from that, I do think you can still make friends. If you are into D&D, there are for sure people around that age that play it. And let's not forget gamers in general. The thing is, you won't get to know them in real life but on the internet.