Non-American here too, but since your perspective is EU, what is Nazi party when the Republican party is far right? Like, far far far right?
Depends on how you define 'right'.
Were they conservative? No, they wanted to upend society and create one that is nothing like anything ever seen before. They were also anti-religion. In many ways, they were anti-tradition, and I wouldn't consider their obsession with bringing back dead traditions to be traditional.
Were they hateful, racist, etc.? Yes, up to you if that's considered 'right'.
Were they, like how American political parties are, friends of big business? Not really, they wanted to sponsor monopolies and whatnot but also wanted the businesses to have no influence over the state, rather the other way around, the state can force the big business to do what they want. As far as if it actually worked that way when they were in power, I'm not sure.