Do all sigma bonds are stronger than pi bonds?
Every possible sigma bond is not stronger than every possible pi bond.

From this table at Wikipedia, we can see that the bond dissociation energy for the F-F bond in $\ce{F2}$ is 157 kj/mol. Meanwhile, the bond dissociation energy for the C-C bond in ethane $\ce{H3C-CH3}$ is on the order of 360 kJ/mol. The bond dissociation energy of the C=C bond in ethene $\ce{H2C=CH2}$ is approximately 710 kJ/mol. The note for this compounds suggests that the pi bond is around 270 kJ/mol (65 kcal/mol), leaving the sigma bond at 440 kJ/mol. Thus, the carbon-carbon pi bond is stronger than the fluorine-fluorine sigma bond.

A general statement of "sigma bonds are stronger than pi bonds" must thus be interpreted in the "all else equal" mode. The relative strength of the carbon-carbon pi bond is less than the relative strength of the carbon-carbon sigma bond. However, just as the strength of the carbon-carbon sigma bond has no bearing on the strength of the fluorine-fluorine sigma bond, the comparison of pi bonds to sigma bonds involving different elements is not helpful. The relative strength of the bonds depends as much or more on the atoms in the bond as it does the type of orbital overlap used to form the bond.