I don't understand incarnation and anatman

I feel like turning to Buddhism as a way to develop compassion and getting free from stress and anxiety. However I am struggling with part of the concepts and this prevents me from going further... For example, I don't understand the sentences that "phenomenon are non existent, non real and only illusions" and the concept of anatman: if phenomenon and people are unreal, how can we help them, interact with them? What should I understand by "there is no I"? I mean what then defines someone's personality, it's opinions, reactions,... ? And then how can we say that there is rebirth if there is no I? By the way, how do you combine a scientific vision of the world with the idea of rebirth and incarnation, since science says that once you're dead, you're just dead and that's. Moreover I understood the Buddha said we shouldn't accept something just out of beliefs, without having experienced it and seen it as true... Which is obviously not the case with the afterlife??

As a concrete example, could someone explain the meaning "the 14th Dalai Lama is an incarnation of the 13th"? What's the difference between the two then?

I guess I sound very confused, but that's the case;-) Any help would be greatly appreciated, thank you all

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