If all edge weights are distinct (no two edges have same weight), is the MST unique?
Yes.
The greedy choice at every step is strictly better than any other choice. There is only one valid set of edges.
How would you find a Spanning Tree with MAXIMUM total weight?
Two ways:
1. Negate all weights and run Kruskal/Prim.
2. Modify Kruskal to sort edges Descending (and skip cycles).