Is it possible for me to delete that screenshot from my post?
You can only edit your post during the first 15 minutes after you posted it. But I reported it to the communitiy hosts and asked for the screenshot to be edited. I see, they already removed the screenshot.
I tried to sign in via iTunes and got the same result.
So it is a wider problem. Do you have any firewalls active that could prevent the communication between your mac and Apple's servers? Kaperski or Little Snitch, or similar? It may be a timeout problem, if your network is slow or is having dropouts.
The iCloud AppleID can behave differently, depending on the service you are trying to use and depending on the country you are in. Is your location set correctly in the system Preferences and location services enabled in System Preferences > Security & privacy?
Did you rename your AppleID recently or changed the password? Then you need to work through this list: https://support.apple.com/en-us/HT204071
Otherwise check at Apple - My Apple ID, if there is any problem.
Added: There has been a server bug for the iCloud servers, that seems to be fixed now: https://9to5mac.com/2017/04/19/50-gb-and-200-gb-plans-vanish-from-icloud-setting s-for-some-users-likely-server-bug/
perhaps the problems you are having, are aside-effect of this problem.