1. I agree.NATO is a region-specific organisation currently. Whether that will change in the future, is anyone's guess. Though I reckon she will stay Atlantic-centric in nature due to the security dynamics that have kept NATO together in the first place.
If and when the EU comes up with a framework for a regional military command, then and only then NATO might have to reassess her role and relevance.
2. The EU has a framework for a regional military command. But it's under-resourced, & floundering around looking for a role, as most of what it might do is already done by NATO. If the USA ever decided to cut its military ties with Europe, then I would expect the EU command to take over NATOs European role immediately.