1) What version of MOO2 does GOG install?

2) How can I tell what version I'm running?

3) As someone who's played thousands of hours of Civ, dabbled some in MOO1, but barely touched MOO2, should I use the unofficial 1.5 patch?

1.

Dos english: 1.40b23 (this is a fan patch, too)
Windows: 1.3
other languages afaik: 1.3

2. You see it in title screen (see screenshot :) )

3. definitely yes. It has alot of Quality of Life features and doesnt alter the base game too much. For me the most important thing is, it makes gameplay and micromanagement faster. Perss Z in battles you will easily win to make autoplay really fast, make buildinglists for planets what to build and press shift+q to build on every planet acoarding to list or just Q for the actual planet ... just alot smoother and polished MoO2 while not loosing the feeling of the game.
I am very happy that the patch makers put so much effort into it and still developing it.

The 1.50 improved is like what the original developers might have made if they had done more rebalancing and fixing it. I see no reason to play more vanilla than that.