The Moon is revolving around the Earth and its centripetal acceleration is towards the Earth. Does it mean that the Moon is freely falling towards Earth? What is the cause of the Moon orbiting around Earth without falling towards it?
The Moon is freely falling toward Earth, like you say. But it is also moving "sideways" quite quickly, so that it "misses" Earth and passes to the side. And continues to freely fall, and again misses passing to the side. Doing this in a continuous manner is called orbiting (or flying).
To be a bit more technical, it is the angular momentum (and energy) of the Earth-Moon system that prevents a collision. The system "wants" to minimize its energy, which would be achieved by a collision, but angular momentum must be conserved. So the system does the best it can at constantly "trying" to collide, and orbits.
because both objects, the earth and the moon have their own unique gravity force due to their mass., there is a place between the two where gravity works independently that keeps the separated. the moon is not falling towards the earth. actually, from some research I've done. the moon is actually moving away from the earth by 1 1/2 inches a year.. not much really, but over billions of years its pretty dramatic
Almost freely falling. Because you can't exclude the gravitational force by other planets on it.
What do you think of centripetal force and falling? You are associating falling because you are very accustomed to such things. But falling is solely due to an external force acted on to attract towards body, so in simple circular motion when you rotate a stone tied to a thread it does come towards though a force of tension is acting on it because direction of motion is defined by velocity not acceleration or force and change in direction of motion is associated with force which is what is done on the moon and its velocity never comes in direction of force and since this force is always attracting body towards it so its direction will be along a line passing through Earth but velocity never comes in its direction so moon never falls.