Great question! To answer it, first we need to talk about what a "particle" is. When it comes to everyday objects (baseballs, rocks, grains of sand, and so on) we usually think of a "particle" as something with a sharp edge, a definite location, and a definite speed.

It turns out that this picture changes a lot when we start talking about subatomic particles (like electrons, neutrons, and protons). Quantum mechanics (which is the best theory of subatomic particles we have) tells us that "particles" aren't just particles; they're also waves! And like waves, subatomic particles don't have a definite location, speed, or size. And here's the key point: the wavelength of a wave can change depending on how much energy it has (this of ripples on a pond: if you splash your hand in the water really fast, you get lots of ripples close together, but if you slowly bob your hand up and down in the water, you get waves that are spaced further apart). It turns out that the wavelength of a subatomic particle gets smaller and smaller as you give it more and more energy. So, to answer your question: a particle can be as small as you want! You just need to be able to give it enough energy to make it that small.

Typical size of an atom is 0.000000001 inch , but the atom itself is made of still smaller bits called quarks. These have a size around 0.000000000000000001 inch!!!!

It depends what you consider a "particle." In general, when we talk about particle, we mean something with mass that's made of atoms. Sometimes these particles are large (like dust particles), and sometimes these particles are small (like nanoparticles). In this common definition, the smallest particle would be an atom.

Good question. There are several possible answers, but the reality is that really small particles behave in some ways like particles and in some ways like waves, which makes giving the particles attributes such as size difficult.

Particles do have something called a Compton wavelength, which is the amount of space in which a particle can be found, which in a sense is like a size in that you can't cram a particle into a volume smaller than its Compton wavelength. However, it's not the same as size the way we think of it, because more than one particle can potentially occupy the same space, which isn't true of normal objects (e.g. your body cannot occupy the same space as somebody else's). The more mass a particle has, the smaller its Compton wavelength, and so the smaller a volume it can be forced into

However, Einstein's theory of general relativity, which is currently the best theory of gravity that we have (it replaces Newton's theory), predicts that a black hole should have a point at the very center with zero volume containing all of the mass of the black hole. Quantum mechanics says that this is impossible. Therefore, either relativity or quantum mechanics as we understand them must be wrong. Physicists are still working on this one, and I guarantee whoever solves it is going to get the Nobel Prize.