Yes. If some force were to slow the moon to a complete stop, the earth's gravity would cause it to fall straight down into the earth (this would take a few days since the moon is so far). The same thing would happen to the ISS if its forward motion were stopped for some reason.
> "in case of the moon whats giving it forward acceleration"
"Acceleration" has a different meaning in physics. A better way to express this question is: "What's giving the moon its forward momentum?"
The moon is using "fossil" momentum that was given to it when it formed, which was probably due to a collision between the earth and an ancient small planet billions of years ago. The thing about momentum is that it STAYS WITH an object forever unless something slows the object down.
This is something that Isaac Newton taught us in his three Laws of Motion. He showed that our everyday intuition about moving objects is wrong.
In much of our everyday experience, we notice that things slow down to a stop unless something keeps pushing them. So our intuition is that, when a moving thing is "left alone," it will slow down and stop. But Newton looked at it a different way. He pointed out that, all those slowing-down things aren't really "left alone" at all, but they are being resisted by things like friction and air resistance. He said that if you remove all that resistance, and TRULY left the object alone, it would continue its motion basically forever.
That's the way we look at the moon's motion today. Since there is no air resistance or other friction to slow it down, it just keeps going. Newton called this property "inertia"; the tendency of an object to maintain its state of motion.
> "human was left to float in earths orbit...wil he start to orbit as well, the forward momentum is it given by earths gravity?"
This is an interesting qestion. If the human is initially *completely* stationary with respect to the earth, then gravity will pull him straight down, and he will certainly collide. In that case the earth's gravity certainly gives him extra momentum, but it is pointed straight down!
But if he has *some* initial sideways momentum, his fate may be different. In this case, the earth's gravity will curve his path. His path will be a combination of his initial sideways momentum and the downward influence of gravity. So the question is, how sharply is his path curved? If the gravity is strong and his initial momentum is small, the curvature will be rather sharp, and his path will intersect with the earth's surface (ouch!) On the other hand, if his initial sideways momentum is sufficiently great (and/or gravity sufficiently small), the curvature of his path may be gentle enough that he manages to "miss" the surface of the earth. In that case, he will swing around the earth and come back to his initial position again, and continue around like that in orbit.
(There is also a third possibility: If his sideways speed is *very* great, he will go into a path that does not return to the earth at all. This speed is the so-called "escape velocity".)