In "Den of Thieves", Esposito found out he was alive.

Does Beckett and Castle have a baby?

In the epilogue of the show - seven years after the end of Season 8, Castle and Beckett have three kids, although Beckett hasn't yet run for State Senate, and Castle's writing isn't mentioned.

What episode does Montgomery die in Castle?

In his final episode "Knockout", Montgomery mentions that he was protecting Kate "the way he should have protected her," referring to Beckett's mother.