TADM2E 6.7
From Algorithm Wiki
Part A
Probably yes. Using Kruskal's algorithm, you'll still get the same insertion order of edges, regardless of how much you add or subtract from the edge weighting.
Part B
No. Example would be the following graph:
A -1-> B B -1-> C A -3-> C
Shortest path from A to C is A->B->C.
If we increase all weights by two, shortest path will change to A->C