Regarding the secret room, as it was a Room of Necessity, mightn't it have appeared to Riddle as a room no one else knew about, simply because that was what he needed?

Just lost a post in which I cited a Webchat JK Rowling did for Bloomsbury, answering the hat/sword question:

Su: How did Neville get the Gryffindor sword, is there a link to the hat?

J.K. Rowling: Yes, there is very definitely a link to the hat! Neville, most worthy Gryffindor, asked for help just as Harry did in the Chamber of secrets, and Gryffindor's sword was transported into Gryffindor's old hat — the Sorting Hat was Gryffindor's initially, as you know. Griphook was wrong — Gryffindor did not 'steal' the sword, not unless you are a goblin fanatic and believe that all goblin-made objects really belong to the maker.

Cheers,
Claire