Does anyone know what happens in the game currently when you conquer Horatio pops? Do they retain gene-splicing bonuses in other empires? Do they continue to accrue bonuses from their original empire if it splices more genes? What if you conquer pops from more than one Horatio empire? What if one Horatio conquers pops from another Horatio?

If it is the case that conquered Horatio pops retain their gene-splicing bonuses, I believe this should be changed. There is no other faction affinity that other factions are able to benefit from when conquering that faction's systems, so it seems unbalanced if Horatio alone becomes such a juicy target for conquest.

The best I can remember, if you are a non-horatio faction, conquered horatio lose all gene splice bonus. If you are playing as a horatio and conquer other horatio, I believe they gain all current gene splices you have. 

No you only get +3 food and +2 approval on hot as non Horatio. Gene mod bonuses do not apply. Likewise you cannot use Portals when you conquer Vaulter worlds. 

think of the gene-splicing as a ora effect for your empire, that effect only your horatio pop.
if same one conquer a system with horatio. they dont have the ora effect. so they get normal horatio
if you conquer a system with horatio. your ora now effect them (and if it was an other horatio player, there ora dont effect your pops)

I had a game with friends when we had 2 horatio players. and I was screeming all game long "clone war is coming" xD
and we fought to see how was the true horatio!