Think of the ink being printed ON the page. Venice in the mid-16th century produced "avvisi" or "gazzettes," which were single page. The idea of something being "in" or "inside" of the page is not adequate to refer to the concept of the newspaper, historically. We still retain this saying in English with TV. We would never say: "I saw you in the TV." It's because the mode in which we receive the media is a flat surface, without depth.
Good point, but in Portuguese, you also say "in" the newspaper / TV. I think it comes from the idea that you are "in the news" (information presented); not from the idea of the material used to publish the news (paper / ink). Languages have different ways to express the different ways its native speakers interpret the world.
Prepositions do not match in meaning on a one to one basis. While usually 'in' is equivalent to the English 'in'. And 'su' equivalent to the English 'on'. The Italians use what would seem to literally translate as 'on the newspapers' where in English the idiom would be 'In the newspapers'. So while 'on the newspapers' is the literal translation and accepted, the best translation would be to the closest English idiom 'in the newspapers'. But the Italians use 'su' here. We'd use it in some English situations too. 'I am on the Board of the newspaper publishers' 'I am on the front page of the newspapers'
Not here, I'm afraid. "Negli" would only be used in front of a (masculine) noun beginning with a vowel, for starters, ("Nei" is used for plurals where the noun is masculine and starting with a consonant) but, more importantly, "nel/ nella/ negli/ nei" all mean to physically be "in" the noun; e.g. in the kitchen, in the soup.
Since you can't actually put yourself "in" the newspaper, you have to put yourself "on" its pages, and in Italian that means using "su" + "il" = sul giornale, or "su" + "i" = "sui" giornali.
One of many quirks that you'll learn if you persevere through the lessons and go onto better understanding. I had the same problem a year ago...