Clarifications about acid-base theory Considering the Arrhenius theory of acids and bases: 


Is every existing compound either an acid or a base? 
Why is a compound such as $ \ce {NH_3}$ considered a base, if it doesn't even have an oxygen atom and a base is supposed to release $ \ce {OH-}$ in water?
If $X$ is a base according to Arrhenius theory, will $X$ still be a base according to the other two theories (and the same if $X$ were an acid)?


According to the Brønsted-Lowry theory:


There are no absolute acid and bases, but only acid-base reaction in which one compound acts as a base and the other as an acid. So, is every reaction of two compounds an acid-base one?
Except for water, are there any other substances which in some reactions act as bases while in others as acids?
A couple of thoughts:

There are mainly 3 different definitions of acids and bases:


The Arrhenius formulation: Acid = proton donor in water,  Based = hydroxide ion donor in water
The Brønsted-Lowry formulation: Acid = potential proton donor, Base = potential proton acceptor
The Lewis formulation: Acid = Electron pair acceptor, Base = Electron pair donor


The Lewis definition is the most general, followed by the BL and finally by the Arrhenius definition.

You are right, for example HCl is considered a strong acid in water, but it is very weakly acidic in glacial acetic acid. If you follow the Lewis definition a large number of reactions will be considered acid base reactions. An exception are free-radical based reactions

There are many compounds that are amphoteric, but it really also depends on the definition you use.