I would like to ask: is it possible to have a setup with PlayStation Eye cameras + action cameras (GoPro etc.)?

Explanation: In a smaller room, I would like to use PS eye cameras in corners and action cameras with wider angles on the front side or back side (so action cameras would be closer).
I don't want to use Kinects (30 fps, problems with legs, etc).

No, as they use different workflows - video from PS Eyes is recorded live while with GoPros it's offline recording.
Generally, you can mix different camera models which support the same video mode (resolution + fps). Although this is strongly discouraged because the quality of picture varies between different cameras. And tracking algorithm works better when pictures from all cameras have similar quality.