Backup Structured Data and Unstructured Data seperately in SQL Server - Is it Possible?
No, there's no such direct feature. You would work at the filegroup level, and at that level SQL Server doesn't care whether it is a filestream or something else you have in that filegroup. 

And when you restore a part of the database, you need to have the primary file group (since this contains all metadata) and whatever other filegroups you want. The non-restored filegroups will be "defunct", and will forever have those "ghost" filegroups hanging around (there's no way to delete/remove a defunct filegroup).