There is no .exe file ... so what do I do now?

Rename the file and add .exe at the end. It is supposed to be automatic but sometimes it doesn't kick in.

rename which file? I only got three ... two are .bin and one is the GOGdownloader file ...

That downloader file. Sorry for not being specific.

The setup file is small - re-download it using your browser and run it again.

I just did that actually thats how I got passed my first issue.

If you cannot get past integrity check it means that .bin files are probably corrupt as well. There are lots of issues with GOG Downloader at the moment. Using browser is considered a safer option.

I already tried that but thanks for the help guys!

Might have been a problem in the path between you and the server - Try again is the only advice I can think of - Tedious, but the second try worked for me.