Question

Is most of our solar system empty space?

Answer 1

Yes.

Explanation:

To visualize this, we can do the following thought experiment.

If we scale down the solar system by a factor 1 million, The Sun would be a ball 1.60m across, with Earth (diameter 0.013m) at a distance of 150m. Neptune would be at 4000m (=4km).
The scaled-down solar system thus has a diameter of some 10 kilometers (much more if we take the outer regions in account).
That's a lot of space for one big ball, a couple of much smaller balls, and some dust.