Done as root:

# losetup /dev/loop0 whdd-copy-mode  // where whdd-copy-mode is the file pulled out of the dying HDD /dev/sdc with WHDD.

* Installed multipath-tools which contains kpartx;

done as root:
# kpartx -a

Which allowed accessing to the partitions of the whdd-copy-mode image disk:

# ls -l /dev/mapper/
total 0
crw------- 1 root root 10, 236  1 janv. 20:52 control
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p1 -> ../dm-0
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p2 -> ../dm-1
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p3 -> ../dm-2
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p4 -> ../dm-3
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p5 -> ../dm-4
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p6 -> ../dm-5
#

Created some directories under /mnt to mount each partition:
[root@squirrel mnt]# ls -l sdc/
sdc/:
total 24
drwxr-xr-x 2 root root 4096  1 janv. 21:01 sdc1
drwxr-xr-x 2 root root 4096  1 janv. 21:01 sdc2
drwxr-xr-x 2 root root 4096  1 janv. 21:01 sdc3
drwxr-xr-x 2 root root 4096  1 janv. 21:01 sdc4
drwxr-xr-x 2 root root 4096  1 janv. 21:01 sdc5
drwxr-xr-x 2 root root 4096  1 janv. 21:01 sdc6
[root@squirrel mnt]#

Some devices from /dev/mapper fail to be mounted:
# mount /dev/mapper/loop0p1 /mnt/sdc/sdc1
mount: wrong fs type, bad option, bad superblock on /dev/mapper/loop0p1,
       missing codepage or helper program, or other error

       In some cases useful info is found in syslog - try
       dmesg | tail or so.
#

# mount /dev/mapper/loop0p2 /mnt/sdc/sdc2
#

# mount /dev/mapper/loop0p3 /mnt/sdc/sdc3
#

# mount /dev/mapper/loop0p4 /mnt/sdc/sdc4
mount: wrong fs type, bad option, bad superblock on /dev/mapper/loop0p4,
       missing codepage or helper program, or other error

       In some cases useful info is found in syslog - try
       dmesg | tail or so.
#
#
       
# mount /dev/mapper/loop0p5 /mnt/sdc/sdc5
mount: unknown filesystem type 'swap'

# mount /dev/mapper/loop0p6 /mnt/sdc/sdc6
#

Of course "loop0p5" is the swap partition, which we don't care about. The two partitions 
which we might want to repare are  the one which is related to sdc1 (here loop0p1) and sdc4 (here loop0p4).

The partitions related to sdc2 and sdc6 do mount fine and their content can be accessed.

Next step will be trying to repair the 2 partitions which trigger the errors, with fsck.ext4. 
Trying the '-n' option first, which  works in reading mode only shows there are errors which 
need to be corrected.

However only one partition needs to be checked and if possible fixed. We can see it with "fdisk -l" 
(invoked as root because the hdd file belongs to root)

# fdisk -l whdd-copy-mode

Disk whdd-copy-mode: 37.3 GiB, 40020664320 bytes, 78165360 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: dos
Disk identifier: 0xace22e9e

Device          Boot     Start       End   Blocks  Id System
whdd-copy-mode1       57993214  78163967 10085377   5 Extended
whdd-copy-mode2           2048  16386047  8192000  83 Linux
whdd-copy-mode3 *     16386048  30726143  7170048  83 Linux
whdd-copy-mode4       30726144  57991167 13632512  83 Linux
whdd-copy-mode5       57993216  64342015  3174400  82 Linux swap / Solaris
whdd-copy-mode6       64344064  78163967  6909952  83 Linux

Partition table entries are not in disk order.
#

The partition number 1 is an extended partition containing the other ones. Therefor the "wrong fs type" 
error from the mount command on /dev/mapper/loop0p1 should be normal.

# cd /dev/mapper/
# ls -l
total 0
crw------- 1 root root 10, 236  1 janv. 20:52 control
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p1 -> ../dm-0
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p2 -> ../dm-1
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p3 -> ../dm-2
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p4 -> ../dm-3
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p5 -> ../dm-4
lrwxrwxrwx 1 root root       7  1 janv. 20:52 loop0p6 -> ../dm-5
#

# LANG=C fsck.ext4 -n loop0p4
See the fsck.txt file for the content, which is quite long →
http://meets.free.fr/Downloads/whdd-file-partition-fsck.txt
#

Now, the real job:

# fsck.ext4 -f -y loop0p4
... (many messages)
#

Done:
# fsck.ext4 -n loop0p4 | more
e2fsck 1.42.8 (20-Jun-2013)
home-buntu : propre, 234476/848640 fichiers, 2178724/3407872 blocs
#

(it says the partition is clean).

Therefore:
# mount loop0p4 /mnt/sdc/sdc4/
# cd /mnt/sdc/sdc4/
# ls -l

Everything's there! \o/!

All my partitions saved. Hurrah!