(A)For the case k=n, the induced sub-graph is the graph itself and it has $2n-2$ edges.
(B)Given from the description of the graph,G it has two edge-disjoint spanning trees.
Now there is a theorem which says, The cut-set of a connected graph G must contain at least one edge from every spanning tree of Graph G.
This graph has two edge-disjoint spanning trees and hence, this graph's cut-set would have minimum size of 2.(one-edge from each of the spanning tree). Note that, here we don't mean that the cut-set size is 2, but it means atleast 2.
So, this is true.
(C)Since there are two edge-disjoint spanning trees of G, there are indeed 2 edge-disjoint paths between every pair of vertices.
This is true.