All permabans are final.
As for your refunds. You agreed to the Term of Use before you downloaded the game which states and I will quote it"
Article 2:
Section 2.2. What happens if my account is terminated? (No LoL for you.)
If your account is terminated, you’ll no longer have access to it, including any of the associated data or content (e.g., champions, skins, Riot Points, etc.). You’ll not be entitled to any refunds and we’ll have no liability to you. We also reserve the right to terminate any other accounts you may have created, as well as your access to any other Riot Services (also without any refunds or liability to you).
You understand and agree that using the Riot Services comes with the risk that your account may be terminated or suspended and that, whenever you use the Riot Services, you’ll bear this risk in mind and always conduct yourself appropriately.
So make a new account and don't get it banned this time.