Have a look at https://docs.atlassian.com/jira/REST/server/ which lists all the REST calls you can make.
From memory, there isn't one for "fields associated with project", because it's not a simple question. Do you mean by field context? What if the field configuration hides it? What if there are several contexts with different options? What if it's valid, but not on screen, or on a screen but hidden? Finally, fields:project is not how it works, it's fields:issuetype-in-project
Badges are a great way to show off community activity, whether you’re a newbie or a Champion.Learn more
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG