First of all you should reset the camera.
You may have inadvertently set something that is causing problems.
See page 53 of the User Manual to see how to set the camera to factory settings.

Then go to page 154 of the User Manual and set the File Numbering to Continuous.
Be sure to read the whole page, particularly the last paragraph (in grey) at the bottom of the page.

Date stamp info is on page 60.
Be sure to read the entire page.
Especially the part that says "they can not be deleted"

For toddler type action pictures indoor, you should use flash.