As
@Alexzee said....there does appear to be a 'mirror' problem in the midst of this. I am not entirely sure that the mirror problem (being unable to resolve archive Ubuntu com, and then 5 E’s failed to fetch etc etc.)
It would be reasonable to change mirrors.....perhaps doing that will fix the whole show....maybe not
Click on the Update icon in the system tray (the small 'shield' shape)
Then on Edit....then Software Sources...then insert your password
you will see;
click on line 1.....JUST ONCE
It will begin the arrange the available mirrors in order of speed....fastest down to slowest.
This will take a minute or so....be patient
Select the top one (fastest)
Then repeat this on line number 2
When finished just close it ....no need for reboot....although you can if you wish.
Any improvement?......Does clicking on the Update icon and choosing 'Refresh' bring about a completed, succesful search etc for updates, with no errors ?