For any DFS of a directed graph, is the strongly connected component containing the vertex with the lowest post order number also contains the sink?
The statement is false. Consider the directed graph $G=(V,E)$ where $V=\{1,2\}$ and $E=\{(1,2), (2,1)\}$.
The graph only contains a single strongly connected component, namely $G$ itself. However no vertex in $V$ is a sink.