It's not just the faction borders that matter from terraforming population explosion either, the extra FIDS produced on the better planets is a far more significant factor. Once the "terraforming race" begins, you kinda have to keep up or be left behind anyway, regardless of faction borders - even if they are 50 parsecs away, their FIDS production will quickly outstrip yours if they have a collection of lush terran/jungle/ocean planets for all their planets with full population boosters, and you are still working away with your arctic and desert planets...

According to my observations, the ai is overwhelmingly changing every planet to terran in the endgame. The resulting population grow will push their borders beyond yours and in the end engulf your empire quite easily. This is really discomforting as the only solution to this is to also compete in the terraforming race.

The FIDS values always change when you terraform planets, and those changes can be both positive or negative. In the case you've presented, the planet would lose its food bonus, but will also increase its production.

Yes, you lose the FIDS and replace them with the new planet type.