What items and covenants can lead to multiplayer opportunities

The one and the only use for the Petrified Something is in the tutorial's nest. As mentioned before, the item you will receive in return is randomized. No other relevant uses for the PS are known as of yet.

You do not necessarily need a Cracked Blue Eye Orb to advance in the covenant. By wearing the Guardian's Seal, a ring that you get upon joining the covenant, you can be summoned by members of the Way of the Blue, a different covenant, when they are invaded. Of course, you still need to be human to be summoned.

As for dispensing justice... yeah, you're kinda out of luck there. Games in the Soul series are rather more catering to offensive PvP than defensive PvP or "white knighting". However, there are typically hotzones for PvP in each Souls game. As Dark Souls 2 has only been recently released, the hotzones probably aren't determined yet. Once more people play and get used to the game, these zones will be recognized and you'll have a better time of finding an appropriate area to "deal justice".