Are files and file groups included when doing a full backup? I have a database with 4 files and 2 file groups. According to the size of the files, it's 1TB. However, the backup (non-compressed) is only 350GB. Is this typical? Or, do I need to specifically select every file/file group when doing backups?
A full backup is everything...

SQL Server backups will only contain the actual data in the database. The size of the physical file is the allocated size that SQL Server has for the file, including the free space.

It does however also keep up with the initial size of your files for the database in the backup as well. So when you restore the database the files will be created and attempt to allocate the same amount of space.