I'm preparing to use the FileTable feature in SQL Server 2012, but I'm unclear about how backups work with this feature:
Does a full database backup include
How would I perform the restore of a single file, for example?
Yes it does include the filetable data. From BOL :
You can use the same restore concept and do a point-in-time restore with STOPAT parameter.
For detailed example refer to (Page 319): Backup and Restore for FILESTREAM Databases.