I'm considering creating a custom web app that will use leaflet. People would log in and be able to create new records through a form and perform queries on the rest service through a custom form I will create. The authentication to access the login will be via LDAP but to authenticate to server(which is not federated with portal(we don't use portal) or ldap) I will send a post request to the rest service via a builtin user I have setup(on the backend). Does each person that logs in via our networks ldap need to have their own user on arcgis servers rest service? If so how does the licensing work for that.
You can have multiple users simultaneously logged into the ArcGIS Server REST endpoint and accessing the same, individual ArcGIS Server web service. Just make sure you have enough resources available to support this; this is explained a bit further here in our documentation.
But do those users need a license to create/edit data? Say for example a web app on agol requires users to have a specific license(Field editor, creator, etc) to do those actions. Does server operate the same way?
ArcGIS Server has a different type of security than ArcGIS Online and Portal for ArcGIS (explained further in our documentation here). One of these differences is that your ArcGIS Server users won't need different or additional licenses to create or edit data - you just need to make sure they're assigned the correct role and permissions in ArcGIS Server and they will be good to go in your custom web app.