Why do stars having mass less than 3 X mass of sun do not collapse into black holes?? Is there a way to find out the radius of a black hole if we know the mass of the parent star and vice versa??
I am only answering part I of your question. Please note that following explanation is highly simplified.
A burning star has huge mass mostly of hydrogen and helium. This huge mass creates a gravitational pull which tries to collapse the star to a single point. However the thermal pressure produced by the burning hydrogen mass (nuclear fusion) counter the gravity of star and it remain in gravitational equilibrium. As the fuel of the star burns out its thermal pressure reduces and the star started its first gravitational collapse.
As the star shrink its density, and temperature increases which ignites the burning (fusion) of heavier elements, such as helium, carbon etc. At this stage the temperature of the star is very high and its radius is small. This stage is known as white dwarf.
After a while the residual fuel also starts to burn out and star become colder. Now if the mass of the star is smaller than a certain limit (<0.7 M) M = mass of sun. Then the cold matter is sustained by electron degeneracy pressure and a very low illumination object is formed which is known as brown dwarf. If the mass of white dwarf is more than this limit, the electron degeneracy pressure could not withstand gravity and collapsed into nucleus, and we see a neutron star.
When mass of the star is higher than the Chandrasekhar limit (>1.4 M) then the neutron degeneracy pressure could not balance gravity and the star is collapsed to a singularity known as black hole.
As far as experimental measurement of radius of black hole is concerned we only see the Schwarzschild radius or gravitational radius or event horizon. This size gives an idea of the black-hole mass.
What is actually inside we have only theories and no experimental data.
I hope it will clear some of your doubts.