I'm not sure who define globalization as working together with other countries to be honest. As far as I can recall, globalization is basically the removal of distance between one countries to another, which means they can interact through other means quite easily.
I think what you said there are all the same. But globalization seems the word that has multiple meanings. Maybe the appropriate meaning according to us can only depends on the context. But if I can give a few definition, that is globalization is I think like dominating or domination. That is in selfish terms but the other is the opposite. Globalization can also be like socialization. Building connections globally.
People mentions cultural export, economic partnership, and so on alongside stuff like tariff wars or international sanction since years ago. I feel like OP definition is a bit too limiting and nobody thinks the same way.
Yes. This is what I'm talking about that it can have a multiple meaning. But since we are on the economics section right now, then it is expected that things in the economy are mentioned right there. Things like tariff, export, wars, sanction, etc... OP's definition is limited but I think there are still someone that thinks the same way as him judging on how big the population we have.