Have you also noticed that the date and time are missing from your pictures? If you have set the 'write date' option to OFF then possibly not.
If it is also missing and you have not set the 'write date' option to OFF and as you are losing your language setting as well it may be that the internal rechargeable battery has either gone flat or it is faulty.
This image is taken from the User Guide for your camera. (Click on the image to enlarge it for better viewing)
Try the recommended method of recharging the battery and see it that resolves your problem. If it does not resolve the problem then unfortunately as the 'battery' is most probably a capacitor mounted on the motherboard and not a user replaceable 'battery' per se, the only way to fix it it to open the camera and replace the faulty component.
Here is a link to the Ifixit guide on how to remove the motherboard from your camera. I may be wrong but the round component on the right side of the motherboard may possibly be the capacitor in question. Sony Cyber-shot DSC-HX300 Motherboard Replacement