From what I can find, it wasn't unusual for pyramids in this time period to lack inscriptions, that mostly started later. The great pyramid also contains what very much looks like and is commonly agreed to be a sarcophagus.

As for other empty rooms, they might have been recently found by us, but could have been found before and resealed over this period of several thousand years. Or it's possible that they were initially made and then never used, I don't think this is uncommon in ancient tombs. It is also theorized that some of these rooms were meant to throw of robbers or were used during construction.

It's not much of a mystery, they were looted.

Probably because they were looted.