https://developer.android.com/reference/android/Manifest.per...
It's so commonly requested though, that virtually every app does have it.
But for quite a while you could still read the permissions list in the play store, and see if it used it. And adding the permission would still give you a warning on upgrade (outside the play store anyway). Both of those (I believe) are gone nowadays.
It's obviously going to be requested by most, but its absence can be extremely relevant, e.g. https://play.google.com/store/apps/details?id=keepass2androi...
It is wrong. Internet permission is made of INTERNET and ACCESS_NETWORK_STATE, which are "normal"-level permissions to be specified in the Manifest. Without them, no Internet. Correctly: there are plentiful applications that do not need it.
As far as I know (please correct if this is wrong), there's no such thing as an app with no Internet permissions. All apps can access the Internet without permission, and only additional uses of the Internet (e.g. seeing your WiFi AP name) require special permission.
AFAIK the "Internet" permission many apps requested was actually for this more advanced usage - just to hit a REST endpoint or something required no permission at all.