The game seems to run only in 1024 x 786 resolution, is there a way to change that to 1280 x 1024? Its the native resolution of my monitor, I play most games in this resolution so I want to do it with GalCiv.
Can somebody give me an advice?

There is no way to change the resolution. It is fixed to 1024x768.

Really? What a shame! I thought it should be possible to play it in higher resolutions since the system requirements said "at least 1024 x 768 screen resolution".
I know the 2nd part has the ability to change it. Sadly I became problems with this f**king impulse, the game didn`t recognize that it was a legal copy and didn`t let me play!
Hope, there will be an Impulse free version of part two at GOG!

Take a look at the My Downloads section of the Stardock Store. If you're lucky, you'll be able to download the GalCiv 2 installer directly from there. I'm more hoping for a Steam-free version.

Strange, this website knows my email adress despite the fact that I never was there b4! How come?

Your Stardock account works for all of their websites, because they are all connected. In all likelihood, you created the account when you registered your copy of GalCiv 2.

Did you perhaps use a different email-address when you registered the game? But then, where does this account come from? <_<

In any case, this is getting beyond my knowledge. I can only suggest, that you contact Stardock's support. Maybe they can sort this out.