Though I learned some basic theory about topological vector spaces, I always confused about the definition of weak-$\*$ topology.

Given $x\in X$, let $\phi\_x: X^\*\to \Bbb R$ denote the evaluation map $u\to u(x)$ at $x$.

The weak-$\*$ topology on $X^\*$ is the initial topology associated with the family of all evaluation mpas $\phi\_x: X^\*\to \Bbb R$. Thus, the weak-$\*$ topology is the smallest topology on $X^\*$ for which all evaluation maps $\phi\_x$ are continuous.

1. What is the definition of initial topology, how to understand the first statement?
2. Why the weak-$\*$ topology is the smallest topology on $X^\*$ for which all evaluation maps $\phi\_x$ are continuous?

3.There is also a conclusion: every subset of $X^\*$ which is open for the weak-$\*$ topology is also open for the strong topology. (1)

I want to show that $(X^\*,SOT)\rightarrow (X^\*, \|\cdot \|)$ 
is continuous, but the book I refered mention that "since all evaluation maps are continuous for the strong topology", why can we prove (1) by the reason $"\cdots"$.