Content (e.g. photo) rights murky, to me

1. If you've made the photograph, you'll own the copyright (unless you've transferred it (e.g. by entering it into a competition where the people running it demand copyright over the entered photos).
2. Images on chess.com are not protected against copying e.g. look at greatest-chess-photos; select a photo, right click, copy image.
3. If you copy a photo off the web, it is most probably copyrighted (unless it explictly says it isn't).
4. You may argue that Fair Use provisions allow you to use someone else's photo provided it's not for profit, limited use, not defamatory, etc.

You are doubtless aware that you would typically lower the resolution of any images you post, to avoid giving access to the original high resolution one.