Translation:The book is next to the newspaper.
Excellent question! The short answer is this: you do not put articles before pronouns! :) Μου is a personal pronoun.
The long answer now:
In order to make some sense of this, firstly you need to know that στην=σε+την (=to+the), so what we now use as an article is in fact a preposition+the definite article. Secondly, you need to know that personal pronouns have two forms, one is strong and one is weak. It is possible to use a structure that includes σε+pronoun, but pronouns do not need to be preceded by articles of course. So, you can either say "(Εσύ) Είσαι δίπλα σε εμένα" (σε+strong pronoun form) meaning "You are next to me" word-for-word or "Είσαι δίπλα μου", which means exactly the same thing but uses the weak form of the pronoun and consequently drops σε.
Yes, that is correct. You will find useful help in the tips of *accusative" lesson (https://www.duolingo.com/skill/el/Accusative-Case/tips-and-notes)
I don't know if this can still be helpful (maybe I'm very late), but to set apart δίπλα from κοντά I remember that δίπλα sounds like "double", and when cells reproduce they DOUBLE in number and the daughter cell grows just NEXT TO the mother cell, which, by the way, is a fact haha