Where does the force tangential to Moon's orbit come from? Not sure if I'm correct, but as far as I know, while moon is revolving around, it is unable to reach the Earth because the Earth's gravitational force isn't strong enough for that. This presumes that the moon has a force at a tangent to its current orbit. Since the moon doesn't decelerate or come closer to Earth, it seems to me that this force is continuously applied. Where does this force come from?
I am likely extremely wrong about this, but please don't downvote this question out of existence before it gets answered (unless a similar question has already been answered before).
 A: There is no force tangential to the Moon's orbit.  Instead, there is what's called a centripetal force pulling the Moon in towards the Earth.  Now if the Moon weren't moving, then it would simply fall to the Earth.  However, the Moon is moving around the Earth, so we must take this into account.
Now forces only accelerate or decelerate things in the direction they act.  Let's look at the situation where the moon is moving up.  It has a force to the left (top diagram).  This means we get some more velocity added to the left, and indeed the Moon will start "falling" towards the Earth.  However it's still moving up, as there have been no forces acting to change the upwards velocity.  The net effect is (instantaneously) the Moon's speed is "nudged" a little to the left (bottom diagram).  This process keeps happening in little steps, and the net effect is for the Moon to go in a circle around the Earth, with the force always perpendicular to the velocity.

A: Yes, there is a constant force transversal (i.e. sideways) to the radial vector to the Moon. The reason is: Earth's rotation drags the tidal bulge faster than the angular velocity of the Moon around Earth. So the bulge rotates "ahead" of the Moon. Because the bulge causes an additional gravitational force, the Moon "sees" a gravitationals force with a small sideway component, which causes the sideway acceleration, which in turn causes a small but steady increase of its orbital radius.
A: 
This presumes that the moon has a force at a tangent to its current orbit.

This statement is incorrect. You are assuming that a force is needed to keep up motion. But if you throw a stone from your spaceship in empty space, then that stone will keep flying at the velocity you gave it forever without any forces acting. This is due to Newton's 1st law.
So, think of the moon as an object moving through empty space with no force acting. Which ever speed it has from the beginning, it keeps without a need for a force. It is just flying straight ahead.
Suddenly, Earth appears and start pulling via gravity.

*

*If it appears in front  (or behind), then gravity pulls along with (parallel to, tangential to) the moon's velocity. This will cause an acceleration along with the velocity which will change the speed (speeding up or slowing down).


*If it appears next to the moon, then gravity pulls sideways (perpendicularly). This will not provide a parallel acceleration component, so there will be no speeding up or slowing down. Instead, this will cause a sideways, perpendicular acceleration which will cause curving or turning.


*If Earth appears in front and a bit to the side, then gravity will pull at an angle - not parallel or perpendicularly, but a bit of both. It will cause both of the above components and thus cause both speeding up and curving. This is what we see in elliptic orbits.
Now, in the special case of a circular orbit, gravity happens to always pull perpendicularly. Not tangentially. The gravitational force "turns" along with the curving motion of the moon so that it is always perpendicular. Thus gravity cannot cause any speeding up or slowing down. The speed that the moon happens to have to begin with, it keeps.
So, there is no need for any tangential force to keep the moon moving. Because there is no force slowing in down (ideally). There is only a force turning its path. That is all.
