Basically every language works that way? You can say underquake in English if you like, doesn't have to be Greek. In fact, it might make sense to pick a widely understood language rather than one with ~13 million speakers

"Hypocenter", like "epicenter", is English, not Greek. These words, like many words in English today, are made of Greek components, which is why kids are taught in grade school English class about Latin and Greek roots.

No, not every language works this way, because not every language uses Latin and Greek root-words like this.