After spending a lot of time using Eyes of Death almost everywhere, as well as gathering informations from japanese websites (2ch, Dark Souls jp wiki), I finally understood I little bit more how exactly the Gravelord Covenant works.
Some stuff still remains unclear, but I thought I could share what I've found so far:
> How to curse other worlds?
Of course you have to use the Eye of Death, but it will only work under two conditions: you can only use it when you are in human form AND in an area you didn't complete/didn't defeat the boss. If you use it while undead or in an area you've already completed, nothing will happen (even though your body will still emit some dark aura).
The Gravelord soul sign in a cursed world looks like this:
http://tinyurl.com/4537nw5
> What happens to the player who is sending the curse?
When you are actually sending a curse to other players worlds, you cannot enter the white fog gate leading to a boss of your current area (the option to enter will be grayed out): this is actually a good way to see if the curse is actually working. The best place to try this is the Painted World, where trying to curse other players will work almost all the time.
> What happens in the cursed worlds?
Black Phantom versions of already existing monsters will appear. Even after exiting the area, resting at a bonfire, quitting the game and even dying, the curse will still be working (as long as the player who sent the curse is still online/didn't die in the meantime). In this case, the only way to stop the curse is to find the Gravelord Soul Sign in order to invade his world.
Black Phantom versions of NPC look like this:
http://tinyurl.com/3shxt3v /
http://tinyurl.com/3ze49uy
> How long is the curse?
If after using the Eye of Death the Gravelord decides to quit the game or exit the current area by teleporting from a bonfire/using an item , the curse will be cancelled. As long as no loading screen appears, the curse will still be working. The curse will also be cancelled if the Gravelord dies.
> Other stuff:
-While the player is cursing other worlds, since he is in human form he can also be invaded by Black Phantoms/Blue Phantoms from other covenants, as well as the "spirit of revenges" (cursed players who found the soul sign of the Gravelord).
-Players can be cursed by a Gravelord in an area they have already completed.
-Cursed players don't have online restrictions (they can use the white soapstone, an eye of death if they have one, etc.).
-When using an Eye of Death, Gravelords cannot see white soul signs / dragon soul signs, etc. anymore, but they can put their own white soul sign.
-When using an Eye of Death you cannot see your own Gravelord soul sign. According to 2ch's Dark Souls boards, apparently the Gravelord soul sign doesn't stay still in the cursed players worlds and is moving (sounds weird...).
-Eyes of Death are rare drops from cursed frogs. Other than that, only 9 can be found normally during the game: 3 in the catacombs, 3 in the Tomb of Giants, 3 from Patches.