When should I use "in the Internet" and when "on the Internet"?
I suppose the large number of "in" prepositions in the phrase can be explained like this: in many languages, including Russian we use the preposition which can be translated into English as "in". So what people often do when they don't know what the correct way is - they "copy" exactly as it's told in their native language. I guess the number of native speakers who use the Internet is much smaller.
If you're talking about information retrieved from the Internet, people routinely say "it is stored ON the Internet", "I found it ON the Internet", "information ON the Internet is ..." etc.
The only example I can think of where you would use "in" would be a phrase like, "I am interested in the Internet".
As noted in response to AmiroucheDouda's post, you might use "in" when "Internet" is used as an adjective to modify some other word. Like, "We live in the Internet age", "In an Internet-based system, access is ...", "Thinking in Internet terms ...", etc.
As in this other thread I would use "in the internet" in the context of Application Programming Interfaces, or APIs. While an Average Joe user reads content off the "front" of an internet website (its Graphical User Interface, or GUI), a function call to an API actually sends a programming thread into the content of the website to retrieve the answer. That retrieval lends a sense of depth, of looking something up in a website, that reading content that's already displayed on the front just doesn't.