What makes Superconductor expel Magnetic lines of force? 
*

*What is it that causes the matter in superconducting state expel
magnetic flux? What exactly happens at the atomic level which causes the expulsion of flux and super-conductance of electrons?

*Do all superconductors expel magnetic flux?

*Does the superconductor absolutely block all of flux that try to pass through it, no matter how strong the flux is?

 A: I cannot answer the first question, but I can do the other two.
Yes, all superconductors expel magnetic flux (Meisner-Ochsenfeld effect). It is part of the definition of superconducting state. Without this property, the material would be just a perfect conductor ($\rho_e \approx 0$) which is different than a superconductor.
The field marginally penetrates the superconductor. This penetration is affected by the geometry of the system and the intensity of the external magnetic field applied. In some cases the presence of impurities in the material will trap the magnetic flux within the material in regions where it is not a superconductor anymore. This is important for applications like levitating superconducting rails.
Given a high/strong enough magnetic field, called critical field strength $H_c$, the superconducting state will be destroyed and the material will make a phase transition into a normal state (normal state would have a lower free energy than the superconducting state). Thereby, losing the properties of field expulsion and zero resistance electrical conduction.
