Given a graph G, does a divide-and-conquer approach work to finding minimum spanning trees?

It's correct, that you don't always get a minimal spanning tree by just connecting Xa and Xb. But it is not necessary, that the edges connecting Xa and Xb have the same weight. See the following example.

Not quite. You should assume a solution and reverse-engineer a counterexample. For example, assume for a graph G, the minimum spanning tree is X.

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