While I don't know all of these, I know that gems of the same type have the same voice because the body of the gem is like a preprogrammed 3d model. gems of the same type have the same model and therefore the same vocal cords. I'm assuming that a model is designed through experimentation, and failed gems were shattered and used in things like the cluster.

1. We don’t know how the Diamonds acted when they were formed, so it’s anyone’s guess if they would be dictators.

2. White Diamond is the first Diamond, and probably formed from some sort of mutation in a stone far out in space which gave it sentience and caused it to create a form.

3. White Diamond was the first gen, and created all the others.

4. All gems of the same type have the same voice because it’s how they’re programmed at birth.

5. The Caste system probably began when the Diamonds created different gems to accomplish different tasks. Tasks of higher importance to the Diamonds would be more valuable, and since certain gems were created to accomplish certain tasks, gems were locked into those tasks and a hierarchy was formed by the Diamonds based on the importance of said tasks.

6. My headcanon is that all gems speak the language of whoever they are speaking to. I personally think that they have some sort of auto-translate function in their gemstones. They have their own independent written language, so it would make sense for them to have a spoken one too.