What's wrong with EA.com account and Polish tld?

Solution 1:

Confirmed as a bug inside EA account support and Origin app for Windows 10 that Gaming Stack Exchange community cannot help with.

Problem no 1 (cannot register EA Account with .pl email address)

If you are stuck with first problem in question (i.e. you cannot register parent account and changing Chrome to Edge or any other browser does not help) then you must click the Get help from an advisor without logging in link to continue. This will ask you for your name etc. and then will redirect you to... Answers HQ, so you hit the wall again.

By using old-good Google I managed to find this page, but ultimately it led me back to the above -- after clicking through you finally land at login page prior contacting EA). So, if you cannot create an account, because your email is falsely claimed as invalid then you're realy stuck. Because, to report that you cannot register an account you must... login to an account.

Problem no 2 (have parent account; can't bind child account to)

The Let us know about problems with a game or your EA Account page says:

From EA Help, you can report a bug or give feedback by clicking Contact Us, choosing a game and platform, then selecting the Report a bug category. Depending on your game, we might direct you to Answers HQ or ask you to email us.

After clicking through all the options (i.e. Origin app > For PC > Report a bug > Report a bug) you are finally redirected to the Select contact option page. You must login in order to continue and after you do so, you are... redirected to Answer HQ and you hit the wall again.

Summary

Using non-Polish email address seems to be the only option in this case. It seems that EA has a huge bug in their system.

Or you may try to use Answers HQ, like I did.