Is it possible to take a map created with ArcGIS online, share it with a group and have the group members edit them off-line?
*Note that I am using a free account and the layers in my map were uploaded from a Shapefile.
In order to create a layer that is capable of offline editing, you will need to publish a feature service in ArcGIS Server or ArcGIS Online. You will require an organization account in order to publish a feature service to ArcGIS Online.
The following documentation will give you some tips on the data requirements for offline editing:
Allow Offline Editing on ArcGIS Online Feature Services
Retrieving data ...