The whole point of the account recovery form is to establish that you are the genuine owner of the account. Google needs to be convinced of this before allowing you to regain access by resetting your password.
So far, you have completed and submitted the form and not provided enough information for Google to be sure that you are the real owner of the account - however, you have been offered additional help by the account recovery team (which does not happen very often!) The 30 cent nominal payment you are asked to make via a credit card is not a "fee" for a password reset - it is a security measure and can help show you are not an unauthorised person (i.e. a hacker) trying to claim the account.
Whether you accept the offer and make personal contact with the team, or continue your recovery attempts unaided is entirely up to you.