ive done some homework about this login issue and i hope this helps you out a little bit : Fix : Failed To Get Game Data From The Server Pokemon Go sry mods i dont know if its allowed to share links from other sites.
1 of my accounts got login error and when i crated new account i couldnt pick its name that means it is not banned ?
Nope. Banned is banned. U can still see your avatar in the gym if it's not been taken down even u were banned.
All my acounts were banned Started 3 more over the past 2 days and one just got banned. I expect the other two to fall once I log in using my phone to check them