I now and always use gzip with nginx but never use it for images. Try to find some adventages/disadventages of that kind solution but nothing found.
Of course I can use client side caching in nginx and set expired days for images - but then first load will be always full load without any optimization.
Soo should I or shouldnt gzip images jpeg png etc. ? What this type of commpresion do - change commpression of images to lower quality?
You don't compress images because images are already compressed. In some cases it can actually make them larger (but I've forgotten the reason why). These are binary formats, similar to videos and you won't gain any benefit.