Contradiction in variation of conductance and conductivity on dilution
You get it wrong. 

With the dilution, both conductance and conductivity ( specific conductance ) proportionally decreases, bound by the conductometer cell constant $G^* = \dfrac{\kappa }{ G}$. 

What increases is molar conductivity $\Lambda_\mathrm{m}= \dfrac{\kappa }{ c}$ toward its infinite dilution value by the Kohlrausch equation $\Lambda_\text{m} =\Lambda_\text{m}^\circ - K\sqrt{c} = \alpha f_\lambda \Lambda_\text{m}^\circ$.



Note that conductance is NOT the ease with which ions move. You confuse it with electrical ion mobility, that is closely linked to the molar conductivity.

In fact conductance and conductivity have nothing to do with ions at all all.
Ionic solutions are just one special case how to manage these general current related quantities.

See conductance   and Conductivity on Wikipedia.