As stated above there two reactions: (1) acid dissociation to hydronium ion and hyproperoxide (very fast but only goes to a slight extent due to its unfavorable equilibrium) ; (2) disproportionation to dioxygen and water (complete but slow in the absence of a catalyst -- there are many -- or light.

It dissociates making water and O2.

H2O2 --> H2O + O2 (unless the eq has been reached :-))

Sure Ali. It dissociates for form water and O2. even though this process can be very slow withot an enzyme.

Not just O2, but (O−O)2–, the peroxide anion.

Yes, it's kinda slow. You can add some catalase to make it faster.

That method is used in microbiology to identify catalase-positive microorganisms (such as staphylococci) - if the bacteria has catalase-activity, then a single drop of hydrogen peroxide to the colony will make it bubble (the O2 produced is the air of the bubble)

H2O2 indeed decomposes spontaneously, that's why companies usually add stabalizers to bottles of H2O2 solutions. What and how much they add depends on the desired product purity.

As André Macherius mentioned H2O2 dissociates forming HO2- and H+. The pKa is 11.75 according to Wikipedia. This is of some importance as the base form is more reactive e.g. in several of the hydrolysis reactions. For this reason commercial H2O2 solutions are usually added some acid (phosphoric) to increase the stability.

As stated above there two reactions: (1) acid dissociation to hydronium ion and hyproperoxide (very fast but only goes to a slight extent due to its unfavorable equilibrium) ; (2) disproportionation to dioxygen and water (complete but slow in the absence of a catalyst -- there are many -- or light.