FFXIII-2 incomplete main menu and missing FFXIII bonuses?

It's strange that you don't have the Eternal Crystal. It is at the inventory, in the first slot of Key Items, at the start of the game (or at least at my earliest save, when the Historia Crux is first unlocked).

I had to look up the "Extras" screen since I'd never heard of it, so take this with a little salt, but according to this answer on a different question, the Extras screen is used for unlocking PS3 XMB themes (or gamer pictures on the XBox 360 version). These are themes which apply to the entire PS3 system - the "main menu" of your PS3 when you press the PlayStation button. One of these XMB themes is the Lightning one, which is gotten by having beaten the original FF13, as you have. But my guess is that it would only even exist if you were playing FF13-2 on a PS3 (and had previously beaten FF13 there, obviously); since you're playing on the Steam version, there just isn't any "Extras" section with XMB themes at all.