For accuracy, time step can get smaller when bodies are closer.

Yes, but this would slow the simulation right down if 2 bodies are very close. I think people sometimes use a 'fudge factor', e.g. if distance < x then treat distance as x.

>'fudge factor'

Maybe that is what the 'softening' parameter relates to?

Yes, the softening factor keeps the forces from getting too big when bodies get close together. Better for the visualization but not very accurate to leave it in.

Better than things flying off to infinity or the whole simulation slowing right down.

What you describe is the Euler method, which is well known for being a comparatively bad choice in most situations. The ODE solver can be selected, the default is RK4, which is a Runge–Kutta method of 4th order, it computes the next time step by combining the values at 4 previous time steps.

I see it now, under the 'Advanced' options.