Why Do the Rebels Have Red Lasers?

If I recall, the color of a blaster bolt (character-scale or starship scale) is determined by the quality of the gas used in it - higher quality gives you green, lower quality gives you red. The Rebellion didn't have access to the highest quality gas, and had to make do with the lower quality ammunition.

Why do Imperial ships have green lasers?

Well the simple answer is that green lasers have more energy than red lasers. Rebels need to pierce storm trooper armor so they use high power green lasers. Storm troopers can get more shots at unarmored rebels using low powered red lasers with out recharging their blasters.

Why are clone blasters blue?

Blue blaster bolts are one of the more unique colors in Star Wars lore. Used primarily in the Clone Wars, blue bolts are gases that have been ionized and work especially well against machinery. This is why the clones primarily used them.