The
only true answer is EVERYTHING
that can be displayed can also be stored - there`s not even the need to take a screenshot. period
If you are concerned with your privacy then ask yourself the (only one!) question: "Do i mind
anybody viewing my content (media, etc.)?" If the answer is "yes" then
don`t post that content online! - There is
no other way!
As for the "watermark apps"... they can help link a picture or video to a name. But as you mentioned above, nothing is safe 100%. And even if watermarks are not removed your (media) files can still be redistributed/uploaded somewhere else (with your watermark included).
Also it is worth to mention that any software (including watermarking software) may contain malware. If it is an online service (or an app that uses one), be aware that the watermark can only be applied after uploading the original unwatermarked media file to that site first. Most of the providers i know are ImO not more trustworthy than any other website and could therefore themselves pose a potential risk!
Also network traffic (and hence the media file that`s being uploaded to such a service) can be intercepted/wiretapped!
If you want to be 100% safe then only take your pictures with a ("old-fashioned") "stand-alone" cam and never with your smartphone. Store them for private use, only on computers that are not connected to the internet, EVER! Sad but true.