P: Desktop: "error while checking disk space"

I had to contact services and have them manually control my computer just to fix it... to me a whole 6 hours to get it sorted out... no idea how the fixed it though... bloody ridiculous

As Rikk suggests, it sounds like your Windows account doesn't have the right permissions. It might be easiest to contact customer services by phone/chat so they can log into your computer and help you fix it.

this is my personal laptop, no administrator no networks, my personal

Is your user account on your computer an Adminstrator account? It sounds like you don't have Admin rights. 

no, I don’t have a corporate license, only personal

It sounds like you have a corporate license. You will need to contact your corporate administrator to reinstall. 

I uninstalled the program, installed a creative cloud and there is no application and such a message:

you do not have access to application management, you may need to request permission from your it administrator

Uninstall the Lightroom App.
Restart your computer
Install the Lightroom App

After this check Help>System Info... again to see if you are now on 3.1. 

when I try to update, a message arrives that these are the latest updates