a). The statement is not true.
Zero acceleration doesn't mean that NO forces are present. It only means
that IF there ARE forces present, then they all exactly balance each other,
and their combined effect is the same AS IF there were no forces present.
b). This statement is likewise not true, if air resistance can be ignored.
An object has zero acceleration in any direction where there is zero force,
and DOES have acceleration in any direction where there IS force.
A projectile has zero acceleration in the horizontal direction, because there
is no horizontal force acting on it.
But the projectile has constant downward vertical acceleration, because of
the constant downward vertical force acting on it. Of course, they are the
acceleration of gravity and the force of gravity.