Maximum Spanning Tree vs Maximum Product Spanning Tree
You state several beliefs but no reasoning. In math, if things are true then usually there is a good reason, namely a proof that the thing is true. Don't just make guesses, try to prove that your claims hold.

Regarding your conjecture, consider Kruskal's algorithm, modified so that it arranges the weights in decreasing rather than increasing order. If we apply any monotone increasing function on the weights, the algorithm would make exactly the same choices. Consider what happens when you replace each weight $w$ by its logarithm $\log w$. The weight of a spanning tree containing the edges $e_1,\ldots,e_{n-1}$ is then
$$
\log w(e_1) + \cdots + \log w(e_{n-1}) = \log [w(e_1) \times \cdots \times w(e_{n-1})].
$$
In other words, after replacing all weights with their logarithms, you are actually computing the maximum spanning tree with respect to product. Since both algorithms compute the same spanning tree, your conjecture is correct.