Good questions.
Other than the one we saw in "Snape's worst memory,"
I have no idea.
But it does seem strange to me that he would make such a big deal out of them.
If I really wanted to hide something like that,
I would do it before Harry walked into the office and then put the Pensive out of sight.
I would not do it right in front of him, over and over.
It's like Snape was daring Harry to try for a peek.