The special power only occurs in either space or ground combat during a single activation? Or if I kill a unit in the space combat and one in the ground combat I can copy two tech?
Nekro's TECHNOLOGICAL SINGULARITY:
Once per combat, after 1 of your opponent's units is destroyed, you may gain 1 technology that is owned by that player.
"Once per combat" means once per combat. Once per space combat, and once per ground combat. That's 2 combats, so you can get 2 techs.
Also if I bombard the only unit on the planet during the invasion, does I still trigger a ground combat or not? For copying technology does it count or not? Same thing for their starting tech that lets you spawn a ground force when you win a ground combat?
Ground combat requires 2 players to have ground forces on the same planet. If you bombard the enemy to death before landing, you did not engage in ground combat. Also, if you PDS an enemy fleet to death, or shoot down all landing ground troops with your PDS, there is no combat.
On the other hand, the anti-fighter barrage happens during the first round of combat, so if you destroy a ship that way it counts.