About showing algorithmic gap instance for the Goemans-Williamson SDP
A graph for which $Alg(G) = \beta OPT(G)$ is, by definition, a graph on which the algorithm has approximation ratio $\beta$. You can use this insight to answer the first question.

As to your second question, suppose that $Alg(G) \leq (\alpha_{GW}+\epsilon) OPT(G)$. Since $Alg(G) \geq \alpha_{GW} SDP(G)$, we deduce that
$$
\alpha_{GW} SDP(G) \leq Alg(G) \leq (\alpha_{GW}+\epsilon) OPT(G).
$$
Therefore $SDP(G) \leq (1+O(\epsilon)) OPT(G)$.