How can we say that a proton has some size? How is done that we can determine those things for any sub-atomic patricles? And does is include uncertainty principle?
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How can we say that a proton has some size?
A proton has size since when we fire high energy particles at it, these particles deflect analogously to as if you had a hard sphere of finite radius. We can call the 'size' of the proton the equivalent radius of a hard sphere which would cause (in certain limits) the same scattering.
With protons we can actually associate with it another 'size'. The radius of an atom can be approximated as $A^{1/3}r_0$ where $A$ is the number of nucleons in the atom and $r_0=1.2fm$. We could therefore say the size of the proton is equal to $r_0$ since this would give the same result as this formula.
In summary: We say a proton has size because of how it interacts with other particles. It interacts in such away that we can give the proton an 'effective size' allowing us to use this in calculations instead of having to deal with the complexities of the actual proton structure and quantum mechanical 'fuzziness'.
How is done that we can determine those things for any sub-atomic patricles?
We determine the size of particles, as indicated above, by firing things (like electrons, etc) at them and looking at how these particles scatter from the particle.
And does is include uncertainty principle?
I am unaware of the direct application of the uncertainty principle to this and others may be able to elucidate on the subject.
Keywords to Research
Here are a few key words which you can search the web/books/etc for which may help: cross section, liquid drop model, scattering.
