In regard to Monet - Caesar thought it was Smoker's heart, and stabbed it with intent to kill.
Smoker is a logia, and so is Caesar, so clearly he knew this would kill him. Same would apply to Monet except for one possible ass-pull - her somehow not dying due to her snow powers, since Caesar stabbed her with an icicle.
Difficult to say, we'll have to wait and see.
–- Update From New Post Merge ---
Can we just make a separate poll of people who think Monet is dead or alive? This way, we can laugh at which side is wrong.
In this case, the side that thinks Oda kills characters is wrong.
He already killed far more important characters before, regardless of the circumstances or excuses people like to surround those deaths with.
Past the halfway point the manga has been getting progressively darker as well. So far with OP, the one iron rule is that any rules he makes, he can and will eventually break.
Same can apply here.
Wait and see.
Personally - that icicle (rather than a knife, or any other weapon Caesar could have on him) coupled with her snow powers tells me she is likely not dead.
Than again - it could be a cruel irony on Oda's part - snow woman with a cold heart getting killed by an icicle to that same heart. Either way, I won't be surprised whether she lives or dies, she isn't important to the story.