Best way to perform backups with filegroups and then restore those backups
You cannot restore a single filegroup to an earlier state, because that will leave the database in an inconsistent state.

You can restore a database one filegroup at a time. However, as long as a particular filegroup is not up to date with the PRIMARY filegroup, any access to a table that is stored (even in part) on that filegroup will cause the query to error out. Only after all filegroups are restored to the same level (meaning to the same "log sequence number") can the entire database be accessed.