Do you need the internet to use the apps once you already downloaded and installed them?
Depends on the app. Some use the 'net and otheres do not.
Which apps need the internet and which do not? How do you know which ones need the internet, does the app say whether it is needed or not before you download it?
The app will tell you what permissions it needs before you install, but much of it is thinking about what the app does. If it's a news app or a streaming app it's probably going to require 'net access to work normally . If it's a "make a note to yourself" app it likely will do ok without.
In general, you will want to have 'net access occasionally at least (wifi, if you don't have a data plan) in order to let Market update your apps.
Separate names with a comma.