Backup and restore FileTable files
Does a full database backup include FileTable files?


Yes it does include the filetable data. From BOL :


  When you use SQL Server to back up a FileTable, the FILESTREAM data is backed up with the structured data in the database. If you do not want to back up FILESTREAM data with relational data, you can use a partial backup to exclude FILESTREAM filegroups.


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  How would I perform the restore of a single file, for example?


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.