They don't stop moving because there is nothing to stop them. In our everyday lives, we're used to things stopping after a while if you stop pushing them along. read more
It's because they are moving sideways relative to the sun. The sun is constantly pulling them towards it, but the direction that is "towards the sun" keeps changing as the planet orbits. read more
Planets get hit by and object and start spinning. Suppose you had a basketball on the ground, and it's at a still position. Hit it on its side, and it starts to spin (and move). They don't stop, because there is nothing to make them stop. Here, we have gravity and friction. read more
They did! The current solar system is the stable aftermath of a fairly violent growth period, so what we see now is the result of a several-billion-years-long evolution. read more