Parental restrictions password

If you mean the code to access Settings > General > Restrictions on your iPhone, then was it on the phone when you last backed up ? If not then you can restore to that backup and it should be removed. If it was on the iPhone when you last backed up then the only way to remove it is to reset the iPhone back to factory defaults and you can then re-sync your content back to the phone - you won't be able to restore to the backup as that will keep the code in place.

Will this delete the data already on the phone after the factory setting reset? (iMessages, photos, songs)

Yes, a reset back to factory defaults will remove all content from it, so your music, you downloaded apps and their content, photos, messages will be removed