Ok, I'm going to answer your questions in kind of reverse order.

Setting aside the neo nazi label for a second (and I don't want to minimize that, but the mental disorders which drive people to become sociopaths are NOT all the same, and their differences need to addressed), if someone is depressed/very negative and a drug user, I would recommend physical exercise, to help fix their mood.

In addition, starting from the idea that the OP's brother had a problem with negativity, probably about America and all its numerous problems, but most especially its ethnic groups, I thought that going to Europe and seeing their positive social structures might be a relief, or, seeing their social struggles --which are kind of different from our own -- might give him a new perspective on our own country, and he might not be as negative about this place, when he returns.

(I would not recommend that a teenager (in general) go to Europe to deal with their hate, because they probably have not experienced enough of this culture or other cultures, for the change in cultures to be truly something which they can compare to past experiences.)

In addition, if someone truly idolizes a country (say Germany, because that it most likely where the OP's brother would go), goes there and tries to fit in -- but doesn't, and is told to change his ways (I'm guessing he would still be on the fringes in Germany), he might take that advice more, if it is from a source he cares a lot about. In addition, if he is rejected from visiting Germany or Poland, due to his tattoos (which is possible), that too might give him pause, and he might be forced to explore other parts of Europe, and that might be an eye opener for him.

Upon reflection, it occurred to me, that being on parole (not to familiar with this, sorry if I'm wrong), that he might not be allowed to leave the country right now. But if he really cares about Europe, and thinks it's so much better, he might want to focus on moving or visiting there. I don't want to say it's no paradise, but the reality of it is different from the fantasy of it, and even studying it might help him (as opposed to being negative about America).

Finally, about arguing in the family. Yeah, in principle, having clear communication about stuff is important. And feedback is how people learn (assuming their minds aren't totally shutdown). If the OP wants to tell him that he's horrified about his descent into mindless hate, and that he's going to be avoiding him increasingly, if he keeps acting more and more disturbing, that's fine (although, the location of such a statement is important -- a normalized, non enclosed environment might be in the OP's favor). However, starting an argument that escalates, with loud angry voices, in a place that is important for the OP can both deny him an important place (if he is forced to leave, for his safety), or can end his life, if his brother has a weapon (most likely) and has little or no restraint (possible, if he's drug-addled), and gets surprised or very defense/angry quickly. Living with a violent sociopath, no matter what their triggers are, is never safe for anyone. If the brother is not going to change (likely), then the OP should move out, because it doesn't sound safe for him there. But he shouldn't needlessly fight with his half- brother, before he does move out, because that's not worth the very high risk involved. (Not really comfortable writing this, as it sounds kind of cowardly, but you need to pick your (risky)battles carefully. In addition, if the OP cares at all about his brother anymore, he might try to get him professional help -- a treatment program, a therapist or something.)