This is not true. Like, (almost) at all. (There are a few tiny exceptions, for instance, if an EU national commits child sexual abuse overseas, they can be prosecuted for it in the EU)
Two Germans shooting each other in Australia break Australian law, but not German law.
Ah yes, the notorious extraterritorial "right to be forgotten". Whereby the EU military dispatches its special forces to smash up computers in foreign data centers.
No, that isn't true. To the contrary actually, the GDPR applies to anyone on European soil, even US citizens. When you're on American soil, you fall under American legislation.