Is there any public API document, describing the APIs, use, interaction?
After compiling it you will not need API access. You can access the database as described in the site, by the db file URI.
Do you need some particular feature?
FYI, nanomsg changed their syntax, you can see examples in http://nanomsg.org/v0.1/nn_connect.3.html . I will open another question with general questions i am having in regards to testing how this works.