Abandoning a covenant

I'm a blue knight and yes I have to wear my ring for you to summon me and you must be in human form with your ring on to summon me. I've been summon from random places all across the map, even to areas I hadn't yet been too. The only place I wasn't summon to was the bell tower as that was a pvp area for the protectors of the bell covenant. If you were in that area, if you weren't human, if you weren't wearing the ring and one of us wasn't wearing our ring, that is why you couldn't summon one of us.

As for summoning and invasion The way it worked in dark souls 1 and dark souls 2 are different to make it more fair. It depends both on soul level and soul memory. Your soul level is what level you are while your soul memory is based off of how souls you spent on your armor weapon and levels. You can find it in your player status menu. It's to help fight against over powered people fighting under powered people.

Hope this helps and praise the sun.

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".