Well you can turn them off...I'd recommend doing that the first several games you play...it is an option you can see when you click "Game Options" on the game setup screen (the one where you pick your faction)...
You can kill the pirates by wiping out the pirate base (it's a planet close to the sun), but that isn't an easy task, especially if you are being pushed all the way to your HW...
If you are TEC, a few novalith shots will wipe out the pirate base...otherwise, you will have to use a fleet to kill enough pirate stuff to get to the planet, and the siege it until it dies...don't go there unless you have overwhelming force....