I don't think Eden will know about the letters reaching Canada, I don't think she's kept up to date with current affairs or news.
I also don't think she'll inform on Nick in a hurry, I think she's just desperate and lonely and having her head turned by Isaac might satisfy her for a bit. Isaac is clearly young & particularly evil by his treatment of Janine and I think a weak and impressionable teenager like Eden will be drawn to that.
Isaac may end up wanting to 'get rid of' nick. Both Eden and Isaac are young, passionate and volatile, and could cause a lot of damage in an environment like Gilead. (For themselves or for others) they are just teenagers after all.