What does the format command show for partitions? You likely have unallocated space you could use - you might also see D6 and can add the /etc/vfstab entry to mount it on boot.
No, you have two file systems that are using your virtual memory. Unless they are limited in vstab the df shows the available virtual memory - currently 14GB.
A real swap device would state swap in column 4 (FS type) in vfstab.
The obvious candidates for deletion are files in /tmp and any 'core' dump files (files with name 'core') which you should search for as they can be almost anywhere on the system.