Can I restore an uncompressed differential backup after a compressed full backup? If we enable compression on database backups (because the database backup size is huge) but don't enable it on differential which are relatively small in size, will a restore work? Because the full backup is compressed but the differential isn't compressed.
This is really a question for the DBA site but yes, it will work. Compression is transparent when restoring, and the RESTORE command doesn't need any parameter to tell it that a backup is compressed.

Of course you can easily test this yourself.