Lots to unpack here.
> Why do i need to verify my payment methods to download the apps?
The App Store uses a credit card to validate your identity. Since all downloads (both free and paid) are linked to your Apple Account, they want to make sure its you downloading it, and not someone trying to sneak something onto your system.
> Do i need to pay for download the game?
No idea. I don't know what game you're trying to install. Some games are free. Others are paid.
Regardless of the free/paid status of the game, you'll need to be authenticated/validated before you can install.
> Ive tried hundred of times to fill my CVV but after i press continue it says it failed lol
This sounds like a different problem. Assuming the card is valid, and you're entering the right number, there are other reasons why it might be rejected. Ultimately it's the card issuer/bank that validates the CCV number, so it may be worth checking with them. Additionally, if the card has previously been used on the App Store, but associated with fraudulent activity, Apple may reject the card based on bad faith, in which case you'd need to use a different card (I have no idea how (if at all) to get Apple to unblock a blacklisted card).