Hello there! Got into this game since I had an old version on the pc, though now I'm using Joiplay to play it. 

But the problem is, both quick save and save points don't seem to work. Is there any way to "fix" it? 

Dunno anything about joiplay save bugs. Sorry, can't really help you there.

On PC save problems ususally rise when you haven't unrar/unzipped the files. You can't make changes to zip and rar files that's why playing through them on PC doesn't work.