Unable to connect to app store

No, that model cannot be updated any further than iOS 6.1.6. There are no more updates for it.

Your model of iPod was discontinued in 2013, and there are unlikely to be any apps in the store that can be installed on it because most apps require a more powerful iPod than yours. In addition, access to the store (from an iPod) now requires a more powerful iPod because of the extra security steps that have to be used.

However, you can still add music to that iPod, from an iTunes Library. If you have iTunes on your computer (Windows or early MacOS machines), or Finder on later MacOS machines, you can add music to the iPod.

You can buy music from the iTunes Store, using iTunes on your computer and once in your iTunes Library, you should be able to copy that music to your iPod. You can of course, buy music from other outlets (including your CDs), add it to your iTunes Library and then copy it the your iPod.

Which version of iOS is your iPod using?

Unfortunately, you now need iOS 10 or later in order to use the store, even for the apps.