Just to clear stuff up, the starts are orbiting each other VERY closely around each other, only about 0.2 AU, I would say. I was just saying that an orbit around the smaller star is quite impossible at 0.6 AU. The diamond world might be orbiting 0.6 AU FROM THE COUPLE of the stars. The two moons are orbiting the planet, not each other. They are only perpendicular to each other. Quite far apart aswell. I don't see anything impossible with this system. Alright, let's start.
In the early stages of this solar system, two stars formed. One a white-yellow star, with a lifetime of about 3 bil. years and the other an orange star, with a lifetime of about 20 bil. years. The planet on which life as we know it is likely to form, orbits around 2.4 AU from the two stars in the center. A collision with another of the early planets ejected a huge amount of matter into orbit around the planet, forming a large moon, of about the same mass as ours. The other moon used to be a dwarf planet in the inner solar system until it got catched by the planet into orbit. The planet is still heavily bombarded by asteroids, partly due to the chaos of the early phases of this system. This planet passes through a very eccentric asteroid belt. The belt was already quite thinned out by the planet, but it still will be casing problems in the future, surely. The planet, mainly called Genesis by its creators, will face many challenges. Will complex life develop on this planet? Probably not. Will life try to evolve into complex forms? Surely. Let's try!
Planet: Genesis
Mass: 0.95 Earth masses
Diameter: 11858 km
SMA: 2.4 AU
Atmosphere: Nitrogen (80%), Carbon Dioxide (20%), 0.8 ATM
Moons:
Unnamed moon 1:
Mass: 0.012 Earth masses
Diameter: 3446 km
SMA: 403 000 km
Orbital inclination: 28°
Atmosphere: None
Unnamed moon 2:
Mass: 0.007 Earth masses
Diameter: 3177 km (It actually appears to be bigger than the other moon)
SMA: 151 000 km
Orbital inclination: 87°
Atmosphere: None
Now, time to do stuff! By the way, about 1 bil. years passed since the formation of the system.