HDR camera and stabilized video on Galaxy S5 neo I have a rooted Samsung Galaxy S5 neo (SM-G903F). The phone runs original Android 5.1 (only rooted). The camera app does support neither HDR photos nor stabilized video recording.

Is there a way how to do do HDR photos and stabilized video recording? Maybe some 3rd party application that could do it? I would prefer single app for both HDR photography and stabilized video. Post-processing is not an option for me in both cases.
Try Open Camera. It's free also on playstore. Open Camera is based on camera2 API and supports 4K recording (if you're hardware support it too).