Capacitor charging and energy
1)  Because the capacitance remains constant $$E= \frac{1}{2} CV^2$$ can be used to compare the energy stored.  This can be compared for the states \$a\$ and \$b\$.

2)  Again as Elliot Anderson stated $$ i(t) = C \frac{\Delta v(t)}{\Delta t}$$ is the relationship between the voltage and current.  Here the same equation is used for the states \$a\$ and \$b\$.

Just as an aside, the same equations for an inductance are $$E= \frac{1}{2} LI^2$$ and $$ v(t) = L \frac{\Delta i(t)}{\Delta t}.$$