1.) What makes gravity?
The easy answer is that we don't really know what gravity is. Sir Isaac Newton described it very well, but describing is different from explaining. Newton figured out that gravity pulls between any two objects with mass. Remember that mass is the amount of stuff, or matter, in something. The greater the masses the stronger the pull. He also figured out that gravity depends on the distance between the objects, that it gets weaker as the square of the distance. That means if the moon were twice as far away, Earth would pull on it 1/4 as strongly. Three times as far and the pull would be 1/9th. This was very clever for Newton, but he didn't know what gravity is.
Albert Einstein also took a crack at it, describing it as the bending of a space-time continuum (Whoa!) by objects with mass. What he meant was that space, in more than three dimensions, is bent or warped by mass in such a way as to bring massive objects together. Again, this is a description and not an explanation. Gravity has many mysteries wrapped up in it, all of our other forces have opposites, magnets can pull or push, electricity can pull or push, do you think some day somebody, maybe you, will discover the push that comes with the pull of gravity? Or maybe you will be the one to explain gravity! I bet there is a Nobel Prize waiting for the person who does.
2.) Why does the Earth spin?
I like this question! I am tempted to say that the earth is spinning because it was spinning yesterday and it has a lot of inertia. I don't think that answers your question, though.
The earth formed at the same time as the rest of our solar system out of debris (junk) left over after a star or several stars before our sun exploded. All this stuff flying through space was massive enough that gravity started pulling it together toward one big pile in the middle. This was the birth of our sun, but it was not that simple. The solar system is big, it is huge, it is GIGANTIC! The stuff was moving around in all directions, and it would make sense that on the average, there would be no overall rotational bias, or preference to be going one way any more than any other. But just like your kitchen sink or bathtub, there is always a slight preference for one direction or another. In the solar system's case, this might have been pushed along a little by the spin of the Milky Way galaxy. As the Solar System formed, it behaved like the whirlpool in a bathtub. Distant parts that were moving very slowly went faster as they fell closer to the sun. Not only that, but the orbits of the planets as they formed were all in the same direction, just like that whirlpool. The planets are left-overs from stuff that fell but missed hitting the sun and by collisions with other stuff settled into stable orbits.
The planets themselves were formed by stuff falling in on them, and the same thing happened again. A tiny amount of spin very far away was turned into more spin as the object fell closer and hit the earth. This in turn was probably being pushed by the spin of the solar system, as nearly all the planets spin in the same direction. We think the exceptions are planets that started out in the right direction and then were smashed by asteroids or small early planets that turned them to spinning backwards. So Earth was also like a whirlpool in a drain, most of the matter that fell on the planet as it formed had a preference to be spinning in from west to east, pushing our planet to spin in that direction.
Really, the earth is spinning because it was spinning yesterday, and it has a lot of inertia. :)
Here is a question for you: When you fill a sink with water, there are currents flowing in every direction in the water. If you let it sit, eventually those currents will slow down and stop because water has friction. How long do you think you have to wait for the water to be SO still that it won't make a whirlpool when you open the drain? Try it with a sink or tub where you can open the drain without reaching into the water, which will start currents again. Keep track of your results, and record which way the whirlpool spins if you still get one.
