Is the decomposition reaction of nitrogen monoxide to dinitrogen and dioxygen possible?
You should look up enthalpy of formation and enthalpy of reaction in your textbook. Also have a look at (Gibbs) Free energy change on reaction. This will tell you  if the reaction is going to be spontaneous, as it is in this case.
The thermodynamic energies never tell you how fast the reaction will be as these relate only to the starting (reactant) and ending (product) energies. The activation energy, the barrier between reactants and product is unknown to thermodynamics.
Secondly, a catalyst will not change the thermodynamics of the reaction, the starting and ending states are the same, but it speeds up a reaction by allowing the reaction to proceed by an alternative pathway with a smaller activation barrier.