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.