Calculation of equilibrium constant in a gaseous system A ⇌ B + C
Your analysis is correct, except that you don't account for how the the units cancel out in your calculation.

The initial reaction quotient, $Q_P$, is indeed 3, as you have calculated.  And since $K_P$ is 1, the reaction will shift to the left, increasing $P_A$.  Hence Statement-1 is nearly correct.  I say "nearly" because $K_P$ is dimensionless, so it should be 1, not 1 atm (each partial pressure should be divided by whatever you define as the standard pressure, 1 atm or 1 bar -- that's what you've left out of your calculation; you should try this yourself as an exercise).   

Statement-2 is not quite correct, because it says the "equilibrium shifts in the backward direction."  Assuming you are not changing the temperature, the equilibrium does not shift (it's a constant: $K_P$ = 1).  Rather, the reaction  (and thus $Q_P$) shifts in the backwards direction until equilibrium is attained.