Many resets have been done, no help iOS is 8.0. I'm looking in settings and I see 12.7GB Capacity, but 0 bytes available. Not sure what's taking up all the HD space, wife sez she has 3 pics in her pics folder, but settings shows 304 pics. Settings also shows 11 vids, but we don't know where those are to delete. It looks obvious that we need HD availability, just don't know how to go about that...
First things first. To give some breathing room, go into Safari and under history, choose clear history to flush the browser cache. That will give enough back to move around.
Click and hold any application, now X's will appear. Click the X to delete that App. The data saved with that app will go too. This can clear some space off. You can't delete the apps that come with iOS though. Facebook is a pig and you might want to delete that one if you can, at least temporarily until you've got it all figured out.
The videos and photos you describe are all under photos. You might have to change the view once in there, look for an "all photos" or "camera roll" under photos.