Nexus 10 / Android 5: recovery broken, fastboot not working So I have broken the software of yet another Google device, this time a Nexus 10, manta.

What I did:
- tried to install Ubuntu like so. It failed with

2015/07/18 01:20:36 Cache formatting was not successful, flashing may fail, check your partitions on device
2015/07/18 01:20:48 Cannot push /home/&lt;user&gt;/.cache/ubuntuimages/gpg/image-signing.tar.xz.asc to device: free space on /cache/recovery is unknown



the Google system (that is, Android 5.02 I believe) still boots, but 
I can not enter fastboot any more, "adb reboot fastboot" results in reboot of Android, "adb reboot recovery" results in a picture of a gobot with a red exclamation mark in her chest and the line "no command" being shown after some time followed by a reboot of Android, "fastboot devices" never shows anything
I can not USB-push anything with adb (as suggested here), it fails with


.

failed to copy 'recovery-clockwork-touch-6.0.4.7-manta.img' to '/cache/recovery-clockwork-touch-6.0.4.7-manta.img': Permission denied



I can not enter superuser mode (in order to change permissions, remount rw or rectify whatever may be wrong)


.

adb shell
shell@manta:/ $ su
/system/bin/sh: su: not found



Trying to install and flash CWM from Google Play Store results in "An error occurred while flashing your recovery"
Downloading an image to be flashed onto recovery from Android is no good either because it the flash_image command is not found.
"Upgrading" from Android 5.02 (I think) to 5.1 did not change any of this.


In short, the device is not rooted (because of the update?), whatever is on recovery does not work, fastboot does not work, and therefore there is no way to root the device.

Am I correct in assuming that this effectively rendered the recovery partition/image/system unusable while the main system does not allow any modifications to the recovery partition/image/system and therefore fastboot can not be used any more and nothing on the system level can be installed or changed? If not, what must I do?

Also, would I be wrong saying that all those devices including the present one and this one (and I have a third one in the same state) are now little more than spare parts (in spite of being physically fully functioning) because the systems can't be properly used? Is it wrong to assume that Google designs its systems on purpose so that this will most likely happen if someone tries to install something not specifically endorsed by Google?
Some Nexus 10 tablets have a bug ,the fastboot menu is hiden ,the
screen remain blank even when you are actually in fastboot mod to
make sure you don't miss it do the following
Hold Power + Volume Up + Volume Down until the tablet vibrates twice
(once to shutdown, then a few seconds later to acknowledge fastboot
menu). After the second vibration, you should be in the fastboot
menu, although the screen is blank plug the phone to pc it should be
recognized
Now that you have access to fastboot ,you can flash a new firmware or
a custom recovery to get your device to a working stat.