Concerning the fire place, I don't think JKR would give us anything like that.
I chose to ignore it completely.

Riddle's Award had me for a while, but I've heard of a second candidate --
In the Room of Requirement, near where Harry hid the Prince's book,
he found a tiara which some say belonged to Ravenclaw.
This could also be what Voldemort was looking for when he dropped in for that "interview."
Or maybe he left something down in his Chamber of Secrets...