Restoring 4S to factory settings

If you restore to factory settings, you do not put the data back, that would defeat the purpose of restoring to factory settings.

You can sync your content back after restoring.

If your calendar and contacts are maintained on your computer or a cloud service, then they will still be there when you restore the device as new, simply set them up to sync to the device again.

All apps should be in your iTunes library on your computer, syncing them back to the device after the restore will put them all back along with their data.

As for item 4, you're making the assumption that the issue is software related.  IF that were the case, there would be thousands if not millions of postings about the camera, there simply are not.  The most likely issue is that your device either has a settings glitch (which the restore will correct) or a hardware issue which will require a replacment device.