I would like to ask a question to someone who knows about the different versions of KoDP. Is the GOG version same as the original from 1999? Is anything different at all (or removed?), or is it the same but with support for modern Windows?

It's the original v1.7 (518) with compatibility fixes to get the game started.

Beware:
http://www.gog.com/forum/king_of_dragon_pass/change_font_size

More like bullshit. Also, what texts actually gets cut off? I haven't noticed any yet.

Yes, at some places, text get's cut off if you use big fonts, but it's absolutely no problem to correct this.

just play it on fullscreen with the default resolution 640x480, unless you use one of those monitors/tvs that hate anything less than HD res.

that or play it on android.

The Steam version features new/additional/expanded contents from the iOS/Android version.