Are you there dad?

It isn't logic. It is faith, which is effectively the opposite of logic.

And you're even forgetting number three in this solitary threesome: the holy ghost.

They are but they aren't at the same thing. Im not gonna attempt to describe the belief, it's complicated and also there's no solid answer, it's just deemed a mystery. They all make up the same entity in a way I guess but are each seperate

I've always been told that it's separate people, entities, beings but both have divine powers and he are the Children of one and the brothers and sisters of the other.

Different types of Christianity probably believe different things