You are assuming because we use the same word, we feel the same about the experience.
No, the opposite. I assume that we use the same word, but have different understanding of it. Superficially learning a language is not enough, hence the argument of non-translatable words. When we just translate in our head, we don't get a deeper understanding. As cultural foreigners, we need the other aspects such as poetry to understand the predominant culture of the area we live in. If we want to be a real part of the community that is.
Do you think people are born with local culture?
No, they're raised by local culture. The digital aspect is valid, and has some influence and will have more influence but by bit, unfortunately. Some could say the culture is infused by indoctrination. And yes, they would probably do pretty good on those tests. Not in the specific "what does that line mean"? Part, but other things like idioms, symbolism and such, that we first have to learn, but they grew up with.
And this is why all culture dies. All of it eventually gets shaved off.
No, not all. The core remains the same, the core values. The behavior around those values is what changes. In my case, I tried to be more coherent with my values. In other cases, people become more incoherent with their values (the Neonazis you describe for example).
I don't think that culture is just that one thing, fix and unwavering. It's more like the planet earth. The superficie changes, even the tectonics float around, but the core remains for a long time, without addition nor substraction.