Imo he knows about the Will of D and some parts of what happened during the void century, perhaps like you said just the parts that make the WG look good.
Kuzan wasnt the Fleet Admiral though and I dont think he knew anything, Sengoku definitely knows some things and I guess he may have passed his knowledge to Akainu maybe? Or the Gorosei did idk.
Yeah, I think he knows of a vague history that is very biased towards the world government. Him and Sengoku probably have a surface level knowledge of the will of d, but mostly view it as evil/dangerous. He's probably also comfortable with the fact that the world government had to do unsavory things during the void century in order to eradicate said evil. Kind of reminiscent of Iceberg viewing the "demons of ohara" as evil, despite simultaneously being well meaning,
and having unique knowledge about pluton. The wg propaganda is very effective at twisting facts around and convincing people working for the greater good that they are in the right.
All this ambiguity from oda is intentional too. If I take a charitable view of oda, it's because he wants us to experience akainu determining his own sense of what's right and what's wrong. The uncharitable view would be that oda hasn't yet figured out himself where he wants to akainu to stand, and is stalling. Which is something I think oda does much more often than the fanbase readily admits.