If one of the file group disk crashes, then should this incident be
treated as database crash? Will it cause the database to stop working?
If all your data from that disk is in memory, you'll not even notice this crash.
Until a checkpoint attempts to write on that disk, or you need to read from it a new portion of data(if it's not in memory) you'll be able to work without any error.
Will the restore operation (assuming full backup was taken)
automatically create the file groups as configured before the crash?
Your question is not clear.
You can restore certain filegroups from full backup, but if these filegroups are not readonly
you'll not be able to reconcile them with the rest of your database. It will be
only possible if your db is in full
recovery model and you take and restore tail of the log
backup after your full
backup (and may be other log
backups in between).
Here you can read more in details Piecemeal Restores (SQL Server)