The ArcGIS Editor for OpenStreetMap was released under the Microsoft Public License, which allows you to access, modify, and redistribute its source code and derived works. The complete license is available at esriosmeditor.codeplex.com/license.
The ArcGIS Editor for OpenStreetMap uses the OpenStreetMap API, which limits downloads to an area of 0.5 by 0.5 degrees or 50,000 nodes, whichever is reached first. This is usually more than enough to fill an area for editing.
The ArcGIS Editor for OpenStreetMap can work with other projects that utilize the master OpenStreetMap database. The editor's symbology template includes about 35 thematic layers and about 400 features. An exciting part about the editor is that since it's open source, users can contribute new attribute types to the template or extend the template for other OpenStreetMap projects, such as OpenSeaMap, OpenWheelChair, or Humanitarian OSM Team (HOT).
Not currently. We are looking into developing the capability to edit OpenStreetMap data using Esri's template-based framework via Esri's web APIs in various GIS platforms (desktop, server, or mobile).