Does anyone know what version of the game this is?
And also, whether this is the American or English version of the game?

"This game has been patched to the latest official version: 1.1"
About the version, it's the UK.
You should have run a search for the keyword "version", it would have led directly to the answer!

So I take it there are no children in it, right?
Wasn't there a patch that used to remedy the situation?

Yes, it's on NMA, find it in the mods thread (the link to NMA that is).

The Fallout 2 version has childrens in. Haven't tested the Fallout 1 version from here.

If Fallout 1 is 1.1 why does it say 1.2 when freshly installed? Just reinstalled it to make sure that I wasn't hallucinating. This topic brought up doubts about my patch installation in any case.

1.2? Interesting. I think that's the "semi-official" patch.

Maybe the "1.2" is what GoG put in to make it work with XP/Vista?

I've bought both Fallout 1 and 2 from GOG.
I believe F2 does contain children, while F1 does not. However, this did not appear to have any negative impacts on the game (not like F2 where all manner of freaky occurances go down...)
As has been said, mods to restore children can be obtained if you so desire.