in a newspaper or on a newspaper?

1. Can't you say "on a newspaper"? My grammar book's example provides only "in a newspaper", but I seem to have seen "on a newspaper" as well.
2. Can "in the newspaper" mean a general newspaper, any newspaper or a specific newspaper? Or does it depend?

gz158) I read an article on AIDS in a newspaper.

not a teacher

1) You read about things in the newspaper. If you don't want a nasty ring on your desk you put your coffee cup on the newspaper.
2) It depends.

You read the news in a newspaper.
You see/hear the news on the news.

In BrE, the TV show which reports the news is simply known as "the news".