It's listed here that you say 'Niemand anders' or 'Niemand anderes' in nominative (but not sure how to distinguish when either is used): http://www.canoo.net/services/OnlineGrammar/InflectionRules/FRegeln-P/Pron-Indef/Pron-andere3.html?lang=en
If you want to see 'niemand anderes' in action, you can see it here: http://www.linguee.de/deutsch-englisch/search?source=auto&query=niemand+anderes
(One example is about Harry Potter which is neat)
From what I can tell, it is anderes because niemand is generally considered neuter. When niemand is followed by an adjective, niemand itself doesn't change, but the adjective has to take the endings of an unpreceded adjective. Thus for neuter, it is anderes in the nominative and accusative, and anderem in the dative. The genitive is not used. Thus the most common forms are niemand anderes or niemand anderem. These forms seem to be correct throughout the German-speaking world.
In some areas though, it seems that niemand can also be considered masculine, in which case the forms would be niemand anderer in the nominative, niemand anderen in the accusative, and (unchanged) niemand anderem in the dative. However, like I said, this tends to be a dialect. So to be safe and always correct, you should always use the neuter forms.
It is inflected just like a an adjective as said here - http://www.canoo.net/services/OnlineGrammar/InflectionRules/FRegeln-P/Pron-Indef/Pron-andere3.html?lang=en
I feel like here it is not treated so much as an adjective, but rather as an adverb (I know that it isn't). It is not "no other person" but rather "nobody else". "Other" would be inflected as an adjective, but not "else". This is my understanding, please chip in if I am wrong or unrefined.
I am not quite sure about that. According to the literal definitions, in this sentence "niemand" is an indefinite pronoun: http://zip.net/bnrDF6 - and when "niemand" is used as a noun, it is masculine. Also, "anders" is an adverb when it is right after a pronoun or other adverb, which is exactly the case: http://zip.net/byrD9j - so if "niemand" isn't a noun, it is neither the Nominativ nor the Akkusativ case. Please, correct me if I am mistaken.
I don't even know why they put "different" as a suggestion in the translation of "andere". It is misleading especially out of context. It can have this interpretation in English, but it seems rare and I think the meaning is always that of "other". As in "I like different colours than you" (other colours than you do). "Andere" would be mainly "other", "another", "others" in English as in "Das Leben der Anderen" (The Lives of others) which happens to be a good example to remember the word apart from it being an amazing movie. :)
I don't know if they are "must see" but as a cinephile I loved them:
-"Die bitteren Tränen der Petra von Kant" by R.W. Fassbinder (and other films of his) /
-"Der Himmel über Berlin" and others (by Wim Wenders /
-"Lola rennt" and "Der Krieger und die Kaiserin" (by Tom Tykwer) /
-"Das Experiment" (by Oliver Hirschbiegel) /
-"Hundstage" (by Ulrich Seidl) (this one Austrian) /
-"Die fetten Jahre sind vorbei" (by Hans Weingartner) /
-"Gegen die Wand", "Soul Kitchen" (by Fatih Akin) /
-"Good Bye Lenin!" (by Wolfgang Becker) /
-"Die Welle" (by Dennis Gansel) /
If you haven't seen those, I think that would be a good start. They are of different genres. Enjoy! :)
Anderes is an adjective, and adjective change their endings... this post of robert explains why it takes the adjective neutral ending "es".