I just noticed that I'm able to use the Bone Hawk Amulet with another necklace, kinda like the Falmer Helmet + circlet. As I'm playing as a mage, I need enchanted gear to reduce the spells magicka cost. When I'm using an enchanted armor, it reduces in 33% conjuration and 33% restoration spells cost. My ring, necklace and headgear reduces 33% dest and 33% illusion each, granting me 0 magicka cost for destruction and illusion spells.

So then I enchanted a Bone Hawk Amulet to reduce my conjuration and restoration by 33%, the amulet + armor reduces my conj/rest magicka cost by 66%, as I have the half magicka cost perks, it reduces in 83% the magicka cost for my conjuration and restoration spells, which becomes really overpowered when added with the Destruction/Illusion necklace. I can conjure Wrathmen all the time and heal them without worrying about magicka.

Plus, if I used that necklace to create a new fortify alchemy set, I could be able to create some wicked fortify potions. My conjuration and restoration reduction cost would be near 100% and I would be able to improve my armor rate to a ridiculous level. My fortify fire/frost/magick resistance potions would be 100%. It would be like playing on god mode. Is it supposed to be like this or is it a glitch? My character is a common vampire, not a vampire lord yet.

so basically bone-hawk amulet can be a second amulet you wear? that's very interesting... wonder if the same is true for the new ring.

No, the bone hawk ring cannot be used with another ring.