No, there are sub-particles that comprise those particles. Generally, these are semi-spherical in shape, so there must be empty gaps between them. This space isn't air, it's completely empty.

And electrons are both particles and waves of light. WHooah! That's hard to comprehend! Ask Schrödinger's cat, it will tell you more! (If it is alive at that point)

it is my understanding that NOTHING is totally solid. It was explained to me that the smallest particles that science has evidence of (and I don't remember the name of it at this point) they have done calculations on, and its mass doesn't seem to be enough for its volume, which indicates that it is either hollow, or there are smaller parts making it up.

No, these particles aren't totally solid. They make up matter (and therefore have mass), and we know that matter can be in solid, liquid or gaseous state. So the actual particles aren't solid, but they may be in a solid phase.

"Solid" isn't really a meaningful term at the scale at which these particles exist. They are not little round balls, or even bigger round balls. They are merely clouds of probability of differnt sizes. Like clouds in the sky, they look solid from a distance but go all soft-edged and indeterminate when you get up closes. It is the interaction of these clouds that creates the illusion we call solidity. The electron may nor be in a fixed place, but it knows it doesn't want to stay anywhere near another electron - unless it has a nice friendly proton to keep it company. Protons don't like each other either - unless they have roughly the same number of neutrons to keep them company. Netrons don't give a damn about each other, but will happily hang out with some protons - as long as there ae not too many extra protons. The way all of these effects interact leads to quite regular patterns - like the jocks hanging out in one corner of the dance hall, the nerds in another, and the wallflowers all round the edges. Every one of those people may be moving around, but the pattern is the same. And it is that pattern we call solidity: the individual components are moving but the pattern stays the same. And matter - i.e. us - is the pattern, not the components.