MacOS – Can I enable FileVault and then partition the hard drive later

OS X Internet Recovery
Mac models introduced after public availability of OS X Lion include the ability to start up directly from an Internet-based version of the OS X Recovery system. OS X automatically uses this feature when the Recovery System on the hard disk isn't available (such as when your hard disk encounters an issue, or when your hard disk has been replaced or erased).

My setup is a Mac mini 2011 with a DIY Fusion drive (840 Pro + 1 TB Hitachi). The Fusion drive was built on 10.8 and then the machine was upgraded to 10.9.

diskutil list 
/dev/disk0
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *256.1 GB   disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:          Apple_CoreStorage                         255.7 GB   disk0s2
   3:                 Apple_Boot Boot OS X               134.2 MB   disk0s3
/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *1.0 TB     disk1
   1:                        EFI EFI                     209.7 MB   disk1s1
   2:          Apple_CoreStorage                         934.5 GB   disk1s2
   3:                 Apple_Boot Boot OS X               650.0 MB   disk1s3
   4:       Microsoft Basic Data BOOTCAMP                64.9 GB    disk1s4
/dev/disk2
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:                  Apple_HFS Fusion HD              *1.2 TB     disk2

1. When I press alt, I get three entries, Fusion, Fusion, Boot Camp. Either Fusion being selected boots the main OS. Bootcamp boots Windows.

2. ⌘R boots local Recovery HD (not Internet Recovery). I have a choice of Wi-Fi, if I need Internet Recovery.

In your case, is it possible the Recovery HD is damaged?

Two things come to mind - booting from recovery HD might let Disk Utility be more free in changing the filesystem where your OS resides. You could also try removing it using diskutil in terminal:

diskutil unmount disk0s4
diskutil mergePartitions ignored ignored disk0s2 disk0s4

You will want to have a backup or be familiar with command line and also verify that your Macintosh HD is really disk0s2 by reviewing diskutil list before making any changes.

Once the disk0s4 is subsumed by Macintosh HD you may need to expand that to fill the drive:

diskutil resizeVolume disk0s2 R

If done properly on a system with no issues, all the above commands are non-destructive to disk0s2 (presumably Macintosh HD) and the boot volume support. You will need to go in and set your startup disk to the resized volume using System Preferences to avoid a long delay each time you start your Mac as it looks for the old location of disk0s2 from which to boot. The bless command would work to set the boot destination as well.