How to expose angular 2 methods publicly?

Just make the component register itself in a global map and you can access it from there.

Use either the constructor or ngOnInit() or any of the other lifecycle hooks to register the component and ngOnDestroy() to unregister it.

When you call Angular methods from outside Angular, Angular doesn’t recognize model change. This is what Angulars NgZone is for.
To get a reference to Angular zone just inject it to the constructor

constructor(zone:NgZone) {
}

You can either make zone itself available in a global object as well or just execute the code inside the component within the zone.

For example

calledFromOutside(newValue:String) {
  this.zone.run(() => {
    this.value = newValue;
  });
}

or use the global zone reference like

zone.run(() => { component.calledFromOutside(newValue); });

https://plnkr.co/edit/6gv2MbT4yzUhVUfv5u1b?p=preview

In the browser console you have to switch from <topframe> to plunkerPreviewTarget.... because Plunker executes the code in an iFrame. Then run

window.angularComponentRef.zone.run(() => {window.angularComponentRef.component.callFromOutside('1');})

or

window.angularComponentRef.zone.run(() => {window.angularComponentRef.componentFn('2');})