This game seems not so compatible with newer windows versions. Are there "definite" versions that are available online? Or perhaps add-on's to original versions that makes them better to play?

So far this game worked "fine" for everyone on win7-8-10. You can go to discord (link on a left) and find pinned message in #gta-2d channel for cd version, which is technically the fastest to run game on, but it is a bit sloppy and has extra crashes. In some countries you should be able to get it on steam with gta bundle of some kind.

Couple of years ago, R* officially published GTA 1 and 2 on their website, those links don't exist anymore, since they removed it some time in a past. You can also get version 11.44 by googling it, it will be on forums, that would be, however, the slowest for speedrun, due to many glitches patched. Since they did just give away 9.6f for free, it might just be technically fine to download it elsewhere. But that is another story.

To force game into window mode you have few ways of doing so: -running 11.44, it just does set windowed mode perfectly fine -running 9.6f or cd version while your monitor is set to 16 bit, only that way it will go to window mode, even if you select the menu option -running game with dxwnd or something else of that kind, seemed to work for some people, however I can't help you with this