Once I download a certain app(either free or paid) do I have to be connected to an internet to open and access it? Especially the more educative ones like NASA app, or Dinopedia?
There is no clear indication in the AppStore, as to whether an app needs an active internet connection to work. The most reliable source is common sense and a look on the app size. If, for example, you download a navigation system which is only 50MB, than it probably requires an internet connection to work, as the maps will always be laeger than 50MB.
Most of them dont, for example if you want to play games, most of the time if its just a one player you can get away without internet. But if you want to post your scores or play againsts people online than you will require a internet connection