That's a lot of questions, but here we go.
The general idea is that it is warmer closer to the Sun and colder as you go further out. This means that in the inner solar system molecules like water, ammonia and methane tend to stay as gases and not produce grains and clumps and so on. And because they stay in gas form the radiation pressure from the Sun and the solar wind will push them outwards.
Only as far out as the orbit of Jupiter it becomes cold enough for ice to form. Therefore the inner planets accreted from grains containing heavier atoms like oxygen and aluminium and silicon as well as iron and nickel and so on.
Consequently inside the ice limit at 5 AU only small, dense planets can form, with little or no water. So where did the water come from?
Apart from these protoplanets the early solar system had a lot of small stuff, made of rocks and mostly ice. This debris is no longer there, apart from what's left in the asteroid belt or in Saturn's rings or way out beyond Pluto. How come? Well, imagine a small comet coming close to a planet. There are two possibilities: either it's lucky and gets only put on a wildly different orbit until the next close encounter or .... it hits the planet. After a few 100's of millions of years the planets will have cleaned up the space around them.
So that's where the water came from (and maybe life itself, but that's another story).
Now for the Moon. The Moon is much lighter than the Earth and can not hold an atmosphere. So although it was hit by comets just as the Earth was, the water soon evaporated again, back into space.
