Hey there, in this time I found the following resources and how to use it using curl or ajax calls for Spree:
The most of the calls need to use the "X-Spree-Token" you can generate it from admin section eg: http://localhost:3000/admin from user section and is the token you need and also you can use for example the order token, I had problems with the api using that token if you have problems let me know.
Products
index of products 25 first
[shell]curl -i -H "X-Spree-Token: YOUR_TOKEN_ID" http://0.0.0.0:3000/api/products.json[/shell]