my macbook's os x Yosemite version is unarchived. I can do nothing, can not log in with apple id and lot pf problems

The best (and latest) version for your MacBook Pro is Catalina

But for now, you cannot login because of Yosemite does not support 2 factor authentication. So you will need to get a code from a different apple device. And put this code in the place where you normally should put your password

From your iPhone, iPad, or Apple Watch

If your device is online:

1. Go to Settings > [your name].
2. Tap Sign-In & Security > Two Factor Authentication.
3. Tap Get Verification Code.

If your device is offline:

1. Go to Settings > [your name].
2. Tap Sign-In & Security. 
3. A message says "Account Details Unavailable." Tap Get Verification Code.

From (another) Mac

1. Go to Apple menu  > System Settings, then click your name.
2. Click Sign-In & Security > Two-Factor Authentication.
3. Click Get a Verification Code.

When you use this code instead of your password, you can login on Yosemite and go to the App Store to update to Catalina.

Hope this works!

Correction, you have to put your password and a verification code all together

Where do I input the password? The iCloud password or the login password for the MacBook itself ?

thanks