in q3, assuming I use kruskal, in general (how I understand it), the output of kruskal is dependent on way the edge's sort is done, so, is it enough to prove the sort I've implemented and assume that kruskal is working?

in q4: the total sum of the edges in the group E' must be equals to the total sum of the edges in the graph's MST?

edit: fixed the question number, my bad.