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The eidolon evolutions are bonuses to its base natural armor (a natural armor bonus).
Amulets of Natural Armor provide an enhancement bonus, so they stack.
As far as I'm aware, the only restriction with summoners and eidolons is the shared slots limitation, so your eidolon could wear the rings and amulets just fine, but your summoner would not be able to gain the benefits of items worn in those slots.
"Link (Ex): A summoner and his eidolon share a mental link allows for communication across any distance (as long as they are on the same plane). This communication is a free action, allowing the summoner to give orders to his eidolon at any time. In addition, magic items interfere with the summoner's connection to his eidolon. As a result, the summoner and his eidolon share magic item slots. For example, if the summoner is wearing a ring, his eidolon can wear no more than one ring. In case of a conflict, the items worn by the summoner remain active, and those used by the eidolon become dormant. The eidolon must possess the appropriate appendages to utilize a magic item."
They can, but they share item slots with the summoner, IIRC. So if they are wearing an amulet, the summoner is not able to.
Summoner is one weird class. They may not be the most powerful class, but I feel they are the easiest to optimize.
Eidolons can be beastly in physical combat. But their usually lowish Will save hurts them pretty bad.