Is the heart a weak point of a Logia user?
Concerning Monet, she was too terrified by Zoro's killing intent to properly defend herself. When she was cut, you could see her struggling to move in an attempt to put herself back together. She can't and is shivering with a scared and confused expression on her face. Logia powers activate on a mental level, much like Paramecia and Zoan, however Logias rely on their subconscious to activate the power in the even of danger. It's why they can still touch things, when not using it. There are cases when a human can be paralyzed with fear, as was the case of Monet.





Now, for Law, that's actually pretty simple. Law's power creates a field into which he can manipulate all matter as he pleases. So while inside the field, Law had separated the hearts from the user and enclosed them in their own space. It's why they seem to be frozen in ice, which is how the effect is shown.