Im not sure what you mean by diagnose......but if you want to view your partitions sizes and maybe resize them there are a # of programs out there..... I use cfdisk..... or use your install cd's partitioning program.
as for the / partition thats your root partition wich is where linux is installed ......so when you are using linux its already mounted.....
this might also help you
as root
/sbin/fdisk -l /dev/??? will list the partition tables
/sbin/fdisk -s <partition> will list the size
