Questions

1. Does Arcane Mimicry behave like Arcane Echo in that it's possible to get two versions of the same elite spell?

2. Can you cast heals and enchantments on nature ritual spirits?

1) Arcane echo works on a spell you cast. Arcane mimicry works on the elite spell of your target other ally. Assuming that elite spell would actually be useful to you, you could Echo it or Arcane echo it to have multiple copies. At least thats how I believe it works.

2) I have not had experience with spirits but I have been able to heal NPCs that were not my allies. As long as they were yellow dots or green dots it would usually work. I am not sure about enchantments though..

1) Yes, though as Bgnome said it copies the elite of target ally, so if you're trying to get a second copy of an elite, they'd have to be running the same elite you are.
2) Yes.