What normally happens here is your global race rank with them keeps going down and down, until they all attack you on sight. Then none of their stations will let you dock, so its very hard to get it back up. It doesn't normally drift on its own, so you could say they have a permanent memory of how much they like you.
You can kill all their military ships, but they will spawn more from the shipyards. If you kill those, it will take some time, but they too will eventually respawn. In other words, I doubt there is any way to end that war once begun. I just figured in the beginning you intended to have an ongoing war with the Paranid.
I can't answer the last question for sure. I don't think they will literally go on an offensive, but as their ships wander through the X universe they may attack yours when they encounter them.