Firstly, in regard to Lily and James's relationship, there are several things to consider. Whether or not they were close friends, they did live in close proximity to each other for years, and by Remus Lupin's account, James grew up a bit in sixth year which allowed a friendship to develop between James and Lily. They got together in seventh year where they were Head Boy and Head Girl, and they married a little over a year after school ended.
Secondly, as far as Lily's friends, what about Dorcas Meadowes?
Thirdly, I can't say for certain, but I'm fairly sure that one of the Marauders said that no one knew about the Marauders's animagus forms.
And as far as a gift from Lily to James, I really like the idea that Willow Rosenberg had with Lily giving James a cat, and the Potters do have a cat post-Hogwarts.