Why did Apple decide to lock my account and force me to change the password? A few days ago I got a message on my Mac that my Apple account was locked and I had to change my password. I did that, but ever since then, using Apple products has become a nightmare. I have Mac, iPhone, iPad and Apple TV, I'm signed in all of these devices and they are synced via iCloud.

All devices are asking for password multiple times a day, applications also synced via iCloud (for example Notability) can't sync because they detect iCloud not available. Multiple restart happened, I deleted local files, I deleted caches and still not working as it did a few days ago. Why on earth I have to enter multiple times my password on a device when I assume it should be enough (I assume an auth server should be able to serve all auth related requests centrally) only once?

Does Apple lock user accounts frequently and force users to change passwords? If not, then is possible to get some info why they did it in my case?

My account has had this password for a few months, or half a year. It is in use on daily basis for work.
You mentioned that "all devices are asking for password multiple times a day..."

Apple describes the type of message you could possibly receive in their support document If your Apple ID is locked or disabled


  If you or someone else enters your password, security questions, or
  other account information incorrectly too many times, your Apple ID
  automatically locks to protect your security and you can't sign in to
  any Apple services. You can unlock your Apple ID after you verify your
  identity.


If this was a legitimate security concern (which I believe it could very well be), you need to reset (change) your password and even enable two factor authentication.

Now, bear in mind that there are AppleID phishing scams that will tell you that you're account is locked and then provide you a link on which to confirm your account details.  If you clicked on this, you gave away your account info.  Reset it as soon as possible.

Note:  Legitimate firms (banks, Apple, Facebook, etc.) will never send you a link to validate or sign in.  Always go to their site(s) manually.