If $C$ is convex , weakly-closed and norm-bounded $\Longrightarrow$ $C$ is weakly-compact

Question

Let $X$ be a Banach space and $C\subset X$.

$\fbox{1}$ If $C$ is convex , weakly-closed and norm-bounded $\Longrightarrow$ $C$ is weakly-compact ?

$\fbox{2}$ If $C$ is convex , weakly-closed $\Longrightarrow$ $C$ is weakly-compact ?

Anyone knows a book where can study weak-weak*-topology in Banach spaces ?

Any hints would be appreciated.