Is there any reason he is not openly telling Hermione about Dumbledore's time turner?

Why would it benefit him for her to know about it?

and she saw, in the light of the doorway, that he was smiling - or at least half his face was smiling.

Is Quirrell's half-smile a reference to Robin Hanson's picture?

If the light's coming from the doorway, it's one side of his face that's illuminated, not the bottom.

Edit: ...that is a pretty creepy picture, isn't it?