As long as the verb is in the second position, the sentence is considered right. All the other words are placed accordingly.
Because ich is always the subject of a sentence. Deine Zeitung mag mich would be Your newspaper likes me.
Ah I do enjoy knowing Norwegian when learning German, because so much of this is basically the same. Weird learning it through English though :p
In other words, "ich" and "mich" are both first person singular pronouns, but just like in English, you choose one based on the case, or the role it plays in the sentence. "Ich" is the pronoun for nominative case, meaning that "ich" is the "subject of the sentence" as we'd say it in English grammar.
Ich = I Mich = me
Me like the newspaper. - incorrect English I like the newspaper.
The Newspaper likes me. The Newspaper likes I. - incorrect English
I is a subject pronoun, so by definition, it IS the subject when used, making the newspaper be the Direct Object.
German word order is a little loose (except for the Verb), so you must deduce which is the subject and objects by acknowledging the Pronoun cases, such as subject pronouns: ich, du, er/sie, wir, ihr, Sie/sie
What is the advantage of wording the sentence in this way rather than "Ich mag deine Zeitung"?
Sometimes this funny word order is used to emphasize something by stating it first. In this case, there really isn't an advantage.
In English I guess it's the difference between
Are you leaving?
YOU are leaving?
Because then that sentence should be "deine Zeitung mag mich (acc. case of ich)".
"Deine Zeitung mag Ich." Is it correct to write 'ich' capitalized if it is in the middle or at the end of a sentence?
While this structure is acceptable in German, it looks and is strange in English.
That's so funny that you said, "Unless you live in Pennsylvania"!! I am currently living in Germany, but Ich komme aus Pennsylvania und "Your newspaper, I like" sounds like gut Englisch to me. It sounds more direct. But, of course, intuitions vary widely across people and landes.
Well, I'm from PA too, but this is not what most people in the state consider good English.