Cannot log into AppleID on Yosemite

- I have a clean installation of Yosemite

- I user on the Imac but I could not register the user with an apple ID because during installation I was told there was a server error. - check it with this link Apple - Support - System Status

- I have a working Apple Id - is it verified using this link https://iforgot.apple.com/appleid#!&section=appleid

- I suppose I have no icloud keychain, because I have never used icloud, seein as I have not done anything with my apple ID besides registering one - why did you followed these articles to set up iCloud Keychain Set up iCloud Keychain - Apple Support

If iCloud Keychain won't turn on or sync - Apple Support

iCloud Keychain SMS support by country and region - Apple Support

- If I find Catalina to download on the appstore and click download, the appstore asks me to log in again, here the problem is slightly, curiosly different: I give my email and password, the appstore tells me the password or email are wrong, BUT I do get verification codes send via sms, but here I csnnot enter them anywhere, because the appstore doesnt recognize my credentials.

Are you in installation process of Mac OS catalina or if it is successfully installed and can't sign in with App Store If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

See the article Set up your MacBook Pro - Apple Support

Sign in with your Apple ID: Your Apple ID consists of an email address and a password. It’s the account you use for everything you do with Apple—including using the App Store, Apple TV app, Apple Books, iCloud, Messages, and more. It’s best to have your own Apple ID and not share it. If you don’t already have an Apple ID, you can create one during setup (it’s free). Sign in with the same Apple ID to use any Apple service, on any device—whether it’s your computer, iOS device, iPadOS device, or Apple Watch. See Apple Account on Mac.

You avoided the setting up iCloud Keychain , essentially a trusted device is to be added to get code via text , it could be an iPhone or android device .

You signed out Apple ID from Mac , the new Apple ID will be created if you have correct credentials from previous Apple ID account , that means correct answers for respective questions , date of birth , rescue mail address and its password , and iCloud Keychain verification code .

If apple id is signed out , a new user can't be created in users and groups , you created a new Apple ID from web server , but that will be signed only , when previous account credentials are known , also from a Mac maximum limit for creating Apple ID address is three , if its exceeded a new Apple ID won't be signed in , you have to use any three Apple ID already created in past and resign in it .

Updating of Mac from Mac OS Yosemite to Mac OS catalina is not related .

To set up iCloud Keychain , essentially an iPhone is required , arrange it .

( a ) Use an iPhone and sign in with same Apple ID and password in your Mac .

( b ) In iPhone go to settings , iCloud open keychain and click on advanced two options will be shown reset code and reset iCloud Keychain , click on reset iCloud Keychain .

( c ) A verification code will appear on your mobile number through sms and it will prompt to generate a code , think of code and fill up in the field so keychain will be set up in iPhone , write down this code .

( d ) Come to Mac in system preferences > click on iCloud the box of keychain is unchecked , so tap the keychain box , it will show waiting for approval click on option button , enter the passcode that is generated in iPhone , click on confirm .

( e ) Again in iPhone a pop up will appear showing approve or deny for name of Mac to approve for keychain , click on allow .

( f ) In Mac click on option button enter trusted number an sms will come having a verification code , enter it the trusted number will be saved and visible and finally keychain is set in Mac .

Later , if you have borrowed an iPhone , and want to add an android device it can be done change mobile in iCloud Keychain in Mac - Apple Community

Note : the purpose is to get the code , don't mix up iCloud Keychain with 2FA , both work differently .

I''ll try to explain you in very simple words .

I am having a Mac in which Mac OS Yosemite is installed , I signed out from Mac system preferences , initially the iCloud Keychain was never set up , I don't owe an iPhone , and never plan to purchase .

However I owe an android device , I have to erase the hard drive and reinstall Mac OS ( the next version ) , set up iCloud Keychain and add my country , and mobile number see an article How to get old versions of macOS - Apple Support

When new os is installed , App Store will automatically installed Sign in with your Apple ID - Apple Support , its the choice of you to sign in App Store and use it Sign in to the App Store on Mac - Apple Support

Download apps from the App Store on your Mac - Apple Support

Note : make a rule always configure default apple applications , its depends upon your usage and never alter the basic settings , the Mac will work fine .

When iCloud Keychain is set up and working trusted number is added the code will always appear via text message ( sometimes a delay is there ) but it always appear .

In the old thread the Apple ID is signed out from Mac system preferences , at present in your Mac are you using secondary authentication in which iCloud Keychain is set up and not as 2FA , the code for 2FA is quite different .

What is the status for Mac system preferences ? please clarify .

Have you set up iCloud keychain , is the keychain box unchecked in Mac system preferences ?

Have you tried the solutions from the post you linked? Did they work for you?