For the first question, the strong topology is the polar topology generated by all weakly bounded subsets. The weakly bounded subsets of $E$ are also weakly bounded in $E^{\ast\ast}$ since $E\subset E^{\ast\ast}$ and they have the same dual space $E^{\ast}.$ Therefore $\beta(E^{\ast},E^{\ast\ast})$ is finer than $\beta(E^{\ast},E).$