Anything that has mass is affected by gravity. I don't know of any particles that are so small that they can not be affected by gravity.

If you have any two bodies with mass there will be a gravitational attraction between them. So if you were holding, say, two pencils those two pencils would have a gravitational force. The reason that you do not notice this is because the earth is so massive that everything on earth (no where near as massive) feels the gravitation from the earth. This is also the reason that Earth has more gravity than the moon --the earth is more massive than the moon.

I believe that our current understanding of Einstein's relativity is that all particles are affected by gravity. In the theory, since the presence of matter warps space and time, any particle traveling through space is affected whether it is large or small and whether it has mass or does not.

Gravity affects everything equally according to its mass. Therefore, no: a small particle experiences less force, but it needs less force to move it around.

All particles that have mass are affected by gravity. But for many small particles (called Brownian particles) gravity is relatively unimportant and other effects, such as those related to temperature, push the particles around in such a way that gravity seems not to affect them.