Can the thermodynamic predictions of redox reactions based on E and dG contradict each other?
$\Delta G = -n {\mathcal F} \Delta {\mathcal E} $

$\mathcal F$ is Faraday's constant, which physicists currently believe has been constant throughout the universe for all time.  $n$ is the number of electrons transfered in an electrochemical reaction.  For a given reaction, $n$ is also constant in all places and times.

Thus, $\Delta G$ determines $\Delta {\mathcal E}$ and vice versa.  


  Are there any errors in above calculations? 


Yes, there must be.


  According to E∘ values, reaction (2) is more feasible than reaction (1). Am I correct ?
  According to ΔG∘ values, reaction (1) is more feasible than reaction (2). Am I correct ?


Both of these cannot be correct.


  Is it useless to use E values to predict the feasibilities of redox reactions ? 


No, it is just as good and exactly as informative as $\Delta G$.


  Should we always resort to ΔG ?


No.  Feel free to resort to $\Delta G$ if you like units like kJ/mol instead of volts, but other than personal preference there is no reason to prefer one over another.


  Is it possible for predictions based on E values and ΔG values to contradict ?


No. 


  If not how can these results be explained ?


UPDATE: Arithmetic error.

The choice of $n$ is arbitrary.  Once you pick $n$ for a given half reaction, it determines the choice of $n$ for the other half reaction, but that's it.  If you then consider a separate cell with separate reactions, you could write that new cell's equation with an arbitrary $n$.  The $\textbf{mol}$ in $\Delta G$'s units of $\frac{\textrm{ kJ}}{\textbf {mol}}$ is $\textbf{mol}$ of reaction, and thus the value of $\Delta G$ depends on how you write the reaction.  For example you could write equation (b) + (c) as 

$$\ce{10M^3+ + 2 H2O + 2 MnO4- -&gt; 2 Mn^2+ + 10 MO^2+ +4 H+}$$

Now, $n$ is twice as large, so $\Delta G$ is twice as large.  But $\Delta \mathcal E$ is unchanged.  This is because $\Delta \mathcal E$ has a basis of "$\textbf{mol}$" of electrons, not of moles of a reaction of arbitrary scale.  In reality the "$\textbf{mol}$" of electrons is converted to a different units (Coulombs) to make things more confusing.  (Remember, a volt is a joule per coulomb.)

So contrary to what I said above, the sign of $\Delta G$ but not the magnitude of $\Delta G$ is fixed, meaning that whether a reaction is absolutely spontaneous can determined by either $\Delta G$ or $\Delta \mathcal E$, but to compare the relative spontaneity of two reactions, either the $n$ values of the two reactions must be the same and then $\Delta G$ values can be used, or else without worrying about $n$ you could just look at $\Delta \mathcal E$.