Yes. Many worlds is just the Schrödinger equation without the wave function collapse. It makes less assumptions. Falsify the Schrödinger equation, and you have falsified many worlds. However, is the wave function collapse falsifiable? It's one postulate which many worlds doesn't make, and it cannot be confirmed or falsified by experiment.

Exactly.

Any good scientific theory must create falsifiable hypotheses.

Otherwise it’s just a nice story.