When should I use these words properly?
If I say:
International trade center, correct? It depends. If it's a center of trade which deals internationally then it's fine. If you're trying to change the official name of the World Trade Center, then no.
World village, correct? I can't imagine what this is using any of your three words.
Global warranty, correct? It sounds OK though I would expect it to be called an International Warranty. Yours means the same, though.