Trying to reinstall OS X

Hi all,

my Macbook Pro 13" 2010 with OS X Mavericks get stuck and crashed by simple using "space keyboard" to preview a picture. When I tried to turn it on, it wasn't possible to get through the spinning wheel and Apple logo disappeared.

- By rebooting, I used ALT+CMD+P+R to resetting the PRAM, I tried CMD+R to Recovery OS X, SHIFT to Safe Boot, and even ALT to Reinstall OS X and CMD+SHIFT+R to Internet Recovery.

- I got Time Machine Backup, which I can't use to Restore as well because OS X Installer still just "Searching for disks..."

- Then I used Disk Utility: to Verify Disk, Repair Disk, Partition and at the end, Erase to Format Mac OS Extended (Journaled) with a message: "Disk Erase failed with the error: Unable to write to the last block of the device."

Disk Utility missing part under the internal HDD?:

- As last option I used Terminal with the command "diskutil list" with this resolution:

I tried following commnads:

- diskutil unmount force /dev/disk0

- diskutil eraseDisk JHFS+ Test /dev/disk0

- date 042109582011 and current time as well

- disk0 is without GUID_partition_scheme (GPT), EFI and HFS, but Terminal can't recognize the command "sudo" to edit something (/usr/bin:/usr/sbin:/bin:/sbin), and I see also notice "no corestorage logical volume groups found" after put command "diskutil cs list"

...as much I'm Googling, as much I feel more and more lost in this stuff 😕

What I did wrong? It all caused OS X Mavericks? When I got previous version of OS X I have't any problem like this.

Can anybody help me out of this circle please?

Thank you guys in advance for any advises,

desperate Peter 😊