Kosaraju’s Algorithm - why transpose? In directed graph, to find strongly connected components why do we have to transpose adjacency matrix (reverses the direction of all edges) if we could use reversed list of nodes by they finishing time and then traverse original graph.
In other words, we would find finish times of all vertices and start traversing from lowest finish time to greatest (by increasing finish time)? 

Additionally, if we do topological sorting on some DAG, and then reverse edges (transpose adjacency matrix) and do topological sorting again - should we get to equal arrays, just in reversed order?

EDIT:
Algorithm description from other topic:
Correctness of Strongly Connected Components algorithm for a directed graph
Taking the transpose and using the list based on finishing time both together ensure that if you have edge A->B(in original graph) where A and B are simply connected sub-graphs than in second dfs A would have finished before start of B(See that in transposed graph edge is from B->A). If we do not take transpose then this is not ensured.

Example:

1->2

2->3

3->4

4->2

3->5

dfs(decreasing finishing time finishing times):1,2,3,5,4
Now if you start from 4 you will visit 5 through 4->2->3->5. But 4 and 5 are not simply connected.

For the second part you may or may not get reversed arrays depending on the order of supplying vertices.