[Byrne]

(i) towards maximum randomness

Well, randomness is associated with entropy.  The reactants side of this particular equation would possess the most randomness because there are more entities on the this side of the equation and compounds in the gaseous state exhibit a higher degree of randomness than compounds in the solid state do.  Therefore, the reverse reaction is driven by the tendency towards maximum randomness.

(ii) towards minumum energy

I'm not really sure what this means exactly.  Does it have something to do with the fact that the reaction is exothermic and therefore the activiation energy in the forward direction would be less than that in the reverse direction?  

Help...

[Yggdrasil]

Are you talking about in general or for a specific reaction?  Beause entropy does not always favor the reactant side, in general.

[Donaldson Tan]

What drives a reaction is the drive to minimum free energy.

G = H - TS
dG = dH - TdS - SdT
Under isothermal condition, the above equation reduces to:
dG = dH - TdS

For a chemical reaction to occur, dG < 0

From the above equation, one can tell that whether a chemical reaction occurs depends on its enthalpy change and change of entropy.

[Byrne]

I'm sorry, I forgot to actually write the reaction down  

Y(s) + 2N(g) <---> 2Z(s), DeltaH = -800kJ

[Yggdrasil]

(i) Yes, you are correct.

(ii) You're somewhat on the right track, but the explanation does not have to do with activation energy (you only need to consider activation energy for kinetics, not thermodynamics).  The reaction is exothermic so that means that the reaction releases energy.  By the conservation of energy, that energy must have come from the reactants.  So, this means that the products are at a lower potential energy than the reactants.  By the equation geodome posted above, will tend to proceed toward lowering potential energy (much like objects will fall down in order to lower their gravitational potential energy).  So, enthalpy will favor the forward reaction.

In general, enthalpy will favor the forward reaction for exothermic processes while it will favor the reverse reaction for endothermic processes.