Player A has elesh norn, grand cenobite out, player B "casts" Flayer of the Hatebound from his/her graveyard.

Is my understanding correct that flayer comes in as a 2/0, triggers his own ability, then dies when SBAs are checked? If this is the case, since flayer no longer in play, does the 2 damage still hit?
Similarly, if an Ichorid comes into play once a Flayer is in, does it still deal 1 damage? It would technically leave play before doing so, which is the source of my confusion.

Thanks.