Impossible to download games

No difference, it still keeps asking to write the password, on Settings keeps popping up the same small window to reinsert it at each OK pressed while on App Store request it doesn't go on when I tap Next.

Interesting about Payment Methods, I still haven't configured any as for now I don't need this feature, but do you think that if I simply fill in the whole form here on my laptop I'll finally be able to verify my ID once for all on my iPad?

I tried the authentication after filling in Payment Methods page but again no difference. Now I'll explain more clearly, both in App Store (when trying to get a FREE game of course) and in iTunes after entering the password it goes to Terms and Conditions acceptance request but enabling I accept Terms and Conditions and tapping Next does nothing, simply sticks there, while on Settings > iTunes Store and App Store after inserting password and tapping OK it asks again endlessly. I think that I'll be fine to simply go beyond the Terms and Conditions ****, even if on Settings > iTunes Store and App Store the password isn't accepted I don't think it will be a problem as the iPad there shows my mail address so looks logged in correctly despite the password request stupid loop. If you know any other method (like for example plugging to laptop and editing certain files or enter remote commands myself or with an Apple specialist/support team member to do to go past this mess feel free to suggest any. Still, I'm not aware of why from App Store it requests me to authenticate telling that I still haven't used the ID on iTunes, this is crazy, 2 different store purposes at all. Thanks for helping so far.

[Edited by Moderator]

After my second talk with a consultant it seems to be an unsolvable problem of compatibility not being met by my iPad with the latest policies, that's what I think I've figured out. A problem that I never heard nor experienced, nor with my old Android devices, they connect to Google accounts anyway even if they're about or over 10 years old. Time for my Plan B.

When you say “most apps” do you mean apps inside App Store or even built-in ones such as Weather, Photo Booth, Safari and any other pre-installed? In the first case it's understandable, I know that the more my iPad becomes obsolete the fewer apps will stay available for it, but in the second case I'm not sure, mine wasn't about apps themselves, it was a problem of Apple ID verification/broken Verify button/procedure. Looks like that Apple didn't want to let older device to still be able to use their own services as newer devices. Does this mean that everyone that has ancient Apple devices can have my same issue when wanting to verify/authenticate his own Apple ID? If not, my case is unique, totally unknown to anyone.

I have already come from 2 chats with 2 consultants about this very problem, after the first chat I posted this problem here in the Apple Community and then (after more attempts to solve it myself) the second time I seem to have realized that it is an unsolvable issue. But I'm sure that somehow I'll do what I want to do with my iPad, usually there's a workaround or an alternative road.

iPad 2 😐.

Yes, that's what I'd probably do, thanks, I didn't have any experience with Apple products till now so some advice from experts is surely great 😁.