An object accelerates when all the forces acting on it don't add up to zero.
No, it is not harder to accelerate a moving object. The initial motion of the object does not affect the force required to accelerate it further. The force required to accelerate an object depends on its mass and the desired acceleration.
No, it takes the same force to accelerate a moving object as it does to accelerate a stationary object, according to Newton's first law of motion. The force required depends on the mass of the object and the desired acceleration.
A non-moving object in equilibrium does not accelerate or change velocity. It remains stationary and experiences no net force acting on it.
accelerate in the direction of the net force.
If a force is being applied to a moving object, it will change its velocity (it will accelerate) appropriately.
Any force.
An unbalanced force will always make an object accelerate. If the object is at rest, it will start moving.
an object can accelerate both up and down
An unbalanced force will always make an object accelerate. If the object is at rest, it will start moving.
Not all moving objects accelerate. In general, an object will accelerate if there is a net force acting on it. For a ball in the air, this might be gravitation + air resistance; for a moving car (once you turn the engine off) it might be the force of friction; etc.
If forces on an object are unbalanced, the object will accelerate or decelerate. If forces on an object are balanced, the object will stay still or keep moving with the same velocity.
When an unbalanced force acts on an object, it causes the object to accelerate in the direction of the force. This acceleration could result in the object moving faster, slowing down, or changing direction. The object will continue to accelerate as long as the unbalanced force is applied.