IPhone – No memory available on the iPhone 6

I'm surprised nobody has answered this correctly.

The solution is to open iTunes, click on your iPhone, go to the Photos tab, then Sync Photos for the folder that contains the photo and video subfolders you want to sync. Each subfolder will then be sync'ed to your iphone UNDERNEATH the Camera Roll as new Albums, and these are treated seperately than the Camera Roll and will always remain synced.

Furthermore, apps that can access the Camera Roll almost always can also access Synced Albums, so this should really work well for you. I keep a whole bunch of old photos and videos on my iPhone at all times using this method and it works great.

As a bonus, unlike the Camera Roll, these Synced Albums don't get backed up in iTunes, so it won't slow down your Backup like a growing Camera Roll will.

It looks like your best choice is to do an OS restore through iTunes if you can. If that does not work, I'd contact Apple Support.

Also, for the record, videos that you take using the Camera app do not appear in the Videos app, they appear in the Photos app as well (strange, I know).