Alright i am currently Genetarr ( loving the improved mind influence) but i have just finished the Lazuli line.
My goals atm are to finish the Genetarr specific medal ( kill 500 assassins) to unlock a new ship design, before i change races. I am using the Firestalker design atm. So my question is " When i kill all 500 of these assassins to get Nephthys ship design, does it carry over when i change races or is it only unlocked while i am genetar?" I am not looking for assumptions or presumptions just concrete facts.

Once the ship is unlocked it does not matter what race you are you can use it. I have seen it on multiple occasions

It carries over. Someone in my legion has the Incubus design but is not a zolazin.