Hello Kh-1979,
We see you're having an issue with the 'Manage Payments' screen not loading, and we'd be happy to help out.
To start, try a quick restart of the iPod, as this may help with odd issues that crop up: Restart your iPod touch
As this may also be related to an issue with the internet connection, we'd recommend trying to connect to a different, strong Wi-Fi network, and then attempt to load it again.
You can also try managing payment info on the Apple ID website if all else fails: Manage your Apple ID
Cheers.